holderian variational problems subject to integral constraints abstract we prove a necessary stationary condition for non differentiable isoperimetric variational problems with scale derivatives defined on the class of holder continuous functions

fractional variational problems depending on indefinite integrals abstract we obtain necessary optimality conditions for variational problems with a lagrangian depending on a caputo fractional derivative a fractional and an indefinite integral main results give fractional euler lagrange type equations and natural boundary conditions which provide a generalization of the previous results found in the literature isoperimetric problems problems with holonomic constraints and depending on higher order caputo derivatives as well as fractional lagrange problems are considered

approximate controllability of partial neutral functional differential systems of fractional order with state dependent delay we prove the approximate controllability of control systems governed by a class of partial neutral functional differential systems of fractional order with state dependent delay in an abstract space sufficient conditions for approximate controllability of the control systems are established provided the approximate controllability of the corresponding linear control systems the results are obtained by using the krasnoselskii schaefer type fixed point theorem with the fractional power of operators an example is provided to illustrate the main results

leitmann s direct method for fractional optimization problems abstract based on a method introduced by leitmann g leitmann a note on absolute extrema of certain integrals int j non linear mech 2 1967 55 59 we exhibit exact solutions for some fractional optimization problems of the calculus of variations and optimal control

approximate controllability of fractional stochastic evolution equations a class of dynamic control systems described by nonlinear fractional stochastic differential equations in hilbert spaces is considered using fixed point technique fractional calculations stochastic analysis technique and methods adopted directly from deterministic control problems a new set of sufficient conditions for approximate controllability of fractional stochastic differential equations is formulated and proved in particular we discuss the approximate controllability of nonlinear fractional stochastic control system under the assumptions that the corresponding linear system is approximately controllable the results in this paper are generalization and continuation of the recent results on this issue an example is provided to show the application of our result finally as a remark the compactness of semigroup is not assumed and subsequently the conditions are obtained for exact controllability result

a new distance measure for model based sequence clustering we review the existing alternatives for defining model based distances for clustering sequences and propose a new one based on the kullback leibler divergence this distance is shown to be especially useful in combination with spectral clustering for improved performance in real world scenarios a model selection scheme is also proposed

investigations on bent and negabent functions via the nega hadamard transform parker considered a new type of discrete fourier transform called nega hadamard transform we prove several results regarding its behavior on combinations of boolean functions and use this theory to derive several results on negabentness that is flat nega spectrum of concatenations and partially symmetric functions we derive the upper bound n 2 for the algebraic degree of a negabent function on n variables further a characterization of bent negabent functions is obtained within a subclass of the maiorana mcfarland set we develop a technique to construct bent negabent boolean functions by using complete mapping polynomials using this technique we demonstrate that for each l 2 there exist bent negabent functions on n 12l variables with algebraic degree n 4 1 3l 1 it is also demonstrated that there exist bent negabent functions on eight variables with algebraic degrees 2 3 and 4 simple proofs of several previously known facts are obtained as immediate consequences of our work

a recurrent probabilistic neural network with dimensionality reduction based on time series discriminant component analysis this paper proposes a probabilistic neural network nn developed on the basis of time series discriminant component analysis tsdca that can be used to classify high dimensional time series patterns tsdca involves the compression of high dimensional time series into a lower dimensional space using a set of orthogonal transformations and the calculation of posterior probabilities based on a continuous density hidden markov model with a gaussian mixture model expressed in the reduced dimensional space the analysis can be incorporated into an nn which is named a time series discriminant component network tsdcn so that parameters of dimensionality reduction and classification can be obtained simultaneously as network coefficients according to a backpropagation through time based learning algorithm with the lagrange multiplier method the tsdcn is considered to enable high accuracy classification of high dimensional time series patterns and to reduce the computation time taken for network training the validity of the tsdcn is demonstrated for high dimensional artificial data and electroencephalogram signals in the experiments conducted during the study

mechanics with fractional derivatives lagrangian and hamiltonian mechanics can be formulated to include derivatives of fractional order f riewe phys rev 53 1890 1996 lagrangians with fractional derivatives lead directly to equations of motion with nonconservative classical forces such as friction the present work continues the development of fractional derivative mechanics by deriving a modified hamilton s principle introducing two types of canonical transformations and deriving the hamilton jacobi equation using generalized mechanics with fractional and higher order derivatives the method is illustrated with a frictional force proportional to velocity in contrast to conventional mechanics with integer order derivatives quantization of a fractional derivative hamiltonian cannot generally be achieved by the traditional replacement of momenta with coordinate derivatives instead a quantum mechanical wave equation is proposed that follows from the hamilton jacobi equation by application of the correspondence principle

fractional noether s theorem in the riesz caputo sense abstract we prove a noether s theorem for fractional variational problems with riesz caputo derivatives both lagrangian and hamiltonian formulations are obtained illustrative examples in the fractional context of the calculus of variations and optimal control are given

approximate controllability of fractional order semilinear systems with bounded delay abstract in this paper sufficient conditions are established for the approximate controllability of a class of semilinear delay control systems of fractional order the existence and uniqueness of mild solution of the system is also proved the results are obtained by using contraction principle and the schauder fixed point theorem some examples are given to illustrate the theory

sobolev type fractional abstract evolution equations with nonlocal conditions and optimal multi controls this paper investigates the existence and uniqueness of mild solutions for a class of sobolev type fractional nonlocal abstract evolution equations in banach spaces we use fractional calculus semigroup theory a singular version of gronwall inequality and leray schauder fixed point theorem for the main results a new kind of sobolev type appears in terms of two linear operators is introduced to extend previous works in the field an existence result of optimal multi control pairs governed by the presented system is proved finally an example is also given to illustrate the obtained theory

the euler lagrange and legendre equations for functionals involving distributed order fractional derivatives abstract in this paper we extend some fractional calculus of variations results by considering functionals depending on distributed order fractional derivatives using variational techniques we deduce optimal necessary conditions of euler lagrange and legendre type we also study the case where integral and holonomic constraints are imposed finally a numerical procedure is given to solve some proposed problems

dynamic stability analysis of stochastic fractional order memristor fuzzy bam neural networks with delay and leakage terms abstract this paper deals with the uniform stability in mean square of stochastic fractional order memristor fuzzy bam neural networks with delay and leakage terms by employing the ideas of cauchy schwartz inequality burkholder davis gundy inequality analysis technique some sufficient conditions are derived to ensure the uniform stability in mean square of such networks the existence uniqueness and stability of its equilibrium point are also showed two different fractional order derivatives between the u layer and v layer are taken into consideration synchronously with fractional order 1 2

complementary sets generalized reed muller codes and power control for ofdm the use of error correcting codes for tight control of the peak to mean envelope power ratio pmepr in orthogonal frequency division multiplexing ofdm transmission is considered in this correspondence by generalizing a result by paterson it is shown that each q phase q is even sequence of length 2m lies in a complementary set of size 2k 1 where k is a nonnegative integer that can be easily determined from the generalized boolean function associated with the sequence for small k this result provides a reasonably tight bound for the pmepr of q phase sequences of length 2 m a new 2h ary generalization of the classical reed muller code is then used together with the result on complementary sets to derive flexible ofdm coding schemes with low pmepr these codes include the codes developed by davis and jedwab as a special case in certain situations the codes in the present correspondence are similar to paterson s code constructions and often outperform them

further results on generalized bent functions and their complete characterization this paper contributes to increase our knowledge on generalized bent functions including generalized bent boolean functions and generalized p ary bent functions with odd prime p by bringing new results on their characterization and construction in arbitrary characteristic more specifically we first investigate relations between generalized bent functions and bent functions by the decomposition of generalized bent functions this enables us to completely characterize generalized bent functions and mathbb z p k bent functions by some affine space associated with the generalized bent functions we also present the relationship between generalized bent boolean functions with an odd number of variables and generalized bent boolean functions with an even number of variables based on the well known maiorana mcfarland class of boolean functions we present some infinite classes of generalized bent boolean functions in addition we introduce a class of generalized hyperbent functions that can be seen as generalized dillon s ps functions finally we solve an open problem related to the description of the dual function of a weakly regular generalized bent boolean function with an odd number of variables via the walsh hadamard transform of their component functions and we generalize these results to the case of odd prime

new quadrature approach based on operational matrix for solving a class of fractional variational problems this manuscript presents a new numerical approach to approximate the solution of a class of fractional variational problems the presented approach is consisting of using the shifted legendre orthonormal polynomials as basis functions of the operational matrix of fractional derivatives described in the caputo sense and that of fractional integrals described in the sense of riemann liouville with the help of the legendre gauss quadrature formula together with the lagrange multipliers method for converting such fractional variational problems into easier problems that consist of solving an algebraic system in the unknown coefficients the convergence of the proposed method is analyzed finally in order to demonstrate the accuracy of the present method some test problems are introduced with their approximate solutions and comparisons with other numerical approaches

discrete direct methods in the fractional calculus of variations finite differences as a subclass of direct methods in the calculus of variations consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem this article generalizes the same idea for fractional variational problems we consider a minimization problem with a lagrangian that depends on the left riemann liouville fractional derivative using the grunwald letnikov definition we approximate the objective functional in an equispaced grid as a multi variable function of the values of the unknown function on mesh points the problem is then transformed to an ordinary static optimization problem the solution to the latter problem gives an approximation to the original fractional problem on mesh points

a fractional calculus of variations for multiple integrals with application to vibrating string we introduce a fractional theory of the calculus of variations for multiple integrals our approach uses the recent notions of riemann liouville fractional derivatives and integrals in the sense of jumarie the main results provide fractional versions of the theorems of green and gauss fractional euler lagrange equations and fractional natural boundary conditions as an application we discuss the fractional equation of motion of a vibrating string

on concepts of controllability for deterministic and stochastic systems the new necessary and sufficient conditions which are formulated in terms of convergence of a certain sequence of operators involving the resolvent of the negative of the controllability operator are found for deterministic linear stationary control systems to be completely and approximately controllable respectively these conditions are applied to study the s controllability a property of attaining an arbitrarily small neighborhood of each point in the state space with a probability arbitrarily close to one and c controllability the s controllability fortified with some uniformity of stochastic systems it is shown that the s controllability the c controllability of a partially observable linear stationary control system with an additive gaussian white noise disturbance on all the intervals 0 t for t 0 is equivalent to the approximate complete controllability of its deterministic part on all the intervals 0 t for t 0

existence of mild solutions for fractional neutral evolution equations abstract in this paper by using the fractional power of operators and some fixed point theorems we discuss a class of fractional neutral evolution equations with nonlocal conditions and obtain various criteria on the existence and uniqueness of mild solutions in the end we give an example to illustrate the applications of the abstract results

approximate controllability of fractional nonlinear differential inclusions fractional differential equations have wide applications in both physical and social sciences this paper addresses the issue of approximate controllability for a class of fractional nonlinear differential inclusions in banach spaces a new set of sufficient conditions are formulated and proved for the approximate controllability of fractional nonlinear differential inclusions in particular the results are established with the assumption that the associated linear part of system is approximately controllable further the result is extended to obtain the conditions for the solvability of controllability results for fractional inclusions with nonlocal conditions finally an example is presented to illustrate the theory of the obtained result

properties of the katugampola fractional derivative with potential application in quantum mechanics katugampola e print arxiv 1410 6535 recently introduced a limit based fractional derivative d referred to in this work as the katugampola fractional derivative that maintains many of the familiar properties of standard derivatives such as the product quotient and chain rules typically fractional derivatives are handled using an integral representation and as such are non local in character the current work starts with a key property of the katugampola fractional derivative d y t1 dydt and the associated differential operator d t1 d1 these operators their inverses commutators anti commutators and several important differential equations are studied the anti commutator serves as a basis for the development of a self adjoint operator which could potentially be useful in quantum mechanics a hamiltonian is constructed from this operator and applied to the particle in a box model

generalized natural boundary conditions for fractional variational problems in terms of the caputo derivative this paper presents the necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a lagrangian depending on the free end points the fractional derivatives are defined in the sense of caputo

existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions abstract in this paper we shall establish sufficient conditions for the existence of integral solutions and extremal integral solutions for some nondensely defined impulsive semilinear functional differential inclusions in separable banach spaces we shall rely on a fixed point theorem for the sum of completely continuous and contraction operators the question of controllability of these equations and the topological structure of the solutions set are considered too

generalized euler lagrange equations for fractional variational problems with free boundary conditions in this article we are going to present necessary conditions which must be satisfied to make the fractional variational problems fvps with completely free boundary conditions have an extremum the fractional derivatives are defined in the caputo sense first we present the necessary conditions for the problem with only one dependent variable and then we generalize them to problems with multiple dependent variables we also find the transversality conditions for when each end point lies on a given arbitrary curve in the case of a single variable or a surface in the case of multiple variables it is also shown that in special cases such as those with specified and unspecified boundary conditions and problems with integer order derivatives the new results reduce to the known necessary conditions some examples are presented to demonstrate the applicability of the new formulations

substructural regularization with data sensitive granularity for sequence transfer learning sequence transfer learning is of interest in both academia and industry with the emergence of numerous new text domains from twitter and other social media tools in this paper we put forward the data sensitive granularity for transfer learning and then a novel substructural regularization transfer learning model stlm is proposed to preserve target domain features at substructural granularity in the light of the condition of labeled data set size our model is underpinned by hidden markov model and regularization theory where the substructural representation can be integrated as a penalty after measuring the dissimilarity of substructures between target domain and stlm with relative entropy stlm can achieve the competing goals of preserving the target domain substructure and utilizing the observations from both the target and source domains simultaneously the estimation of stlm is very efficient since an analytical solution can be derived as a necessary and sufficient condition the relative usability of substructures to act as regularization parameters and the time complexity of stlm are also analyzed and discussed comprehensive experiments of part of speech tagging with both brown and twitter corpora fully justify that our model can make improvements on all the combinations of source and target domains

characterization of negabent functions and construction of bent negabent functions with maximum algebraic degree we present necessary and sufficient conditions for a boolean function to be a negabent function for both an even and an odd number of variables which demonstrates the relationship between negabent functions and bent functions by using these necessary and sufficient conditions for boolean functions to be negabent we obtain that the nega spectrum of a negabent function has at most four values we determine the nega spectrum distribution of negabent functions further we provide a method to construct bent negabent functions in n variables n even of algebraic degree ranging from 2 to n 2 which implies that the maximum algebraic degree of an n variable bent negabent function is equal to n 2 thus we answer two open problems proposed by parker and pott and by stanica et al

bent function sequences in this paper we construct a new family of nonlinear binary signal sets which achieve welch s lower bound on simultaneous cross correlation and autocorrelation magnitudes given a parameter n with n 0 pmod 4 the period of the sequences is 2 n 1 the number of sequences in the set is 2 n 2 and the cross auto correlation function has three values with magnitudes leq 2 n 2 1 the equivalent linear span of the codes is bound above by sum i 1 n 4 left stackrel n i right these new signal sets have the same size and correlation properties as the small set of kasami codes but they have important advantages for use in spread spectrum multiple access communications systems first the sequences are balances which represents only a slight advantage second the sequence generators are easy to randomly initialize into any assigned code and hence can be rapidly hopped from sequence to sequence for code division multiple access operation most importantly the codes are nonlinear in that the order of the linear difference equation satisfied by the sequence can be orders of magnitude larger than the number of memory elements in the generator that produced it this high equivalent linear span assures that the code sequence cannot be readily analyzed by a sophisticated enemy and then used to neutralize the advantages of the spread spectrum processing

generalized plateaued functions and admissible plateaued functions plateaued functions are very important crypto graphic functions due to their various desirable cryptographic characteristics we point out that plateaued functions are more general than bent functions that is functions with maximum nonlinearity some boolean plateaued functions have large nonlinearity which provides protection against fast correlation attacks when they are used as combiners or filters in stream ciphers and contributes when they are the component functions of the substitution boxes in block ciphers to protection against linear cryptanalysis p ary plateaued functions have attracted recently some attention in the literature and many activities on generalized p ary functions have been carried out this paper increases our knowledge on plateaued functions in the general context of generalized p ary functions we first introduce two new versions of plateaued functions which we shall call generalized plateaued functions and admissible plateaued functions the generalized plateaued functions extend the standard notion of plateaued p ary functions to those whose outputs are in the ring mathbb z p k next we study the generalized plateaued functions and use admissible plateaued functions to characterize the generalized plateaued functions by means of their components finally we provide for the first time two constructions of generalized plateaued functions in particular we generalize a known secondary construction of binary generalized bent functions and derive constructions of binary generalized plateaued functions with different amplitudes

controllability of fractional evolution nonlocal impulsive quasilinear delay integro differential systems in this work the controllability result of a class of fractional evolution nonlocal impulsive quasilinear delay integro differential systems in a banach space has been established by using the theory of fractional calculus fixed point technique and also we introduced a new concept called a u resolvent family as an application that illustrates the abstract results an example is given

generalized fractional controller for singular systems of differential equations abstract in this article we consider a class of singular linear systems of first order and introduce a generalized fractional order feedback controller of caputo type the closed loop system in question is a singular system of differential equations having both first and fractional order derivatives we provide a comprehensive theory for the existence and uniqueness of solutions as well as for the stability of the system with inclusion of the fractional order controller an example of a singular system with a fractional order proportional integral controller as well as an example on a 3 bus power system with inclusion of a fractional order damping controller is given to illustrate our theory

generalized bent criteria for boolean functions i generalizations of the bent property of a boolean function are presented by proposing spectral analysis with respect to a well chosen set of local unitary transforms quadratic boolean functions are related to simple graphs and it is shown that the orbit generated by successive local complementations on a graph can be found within the transform spectra under investigation the flat spectra of a quadratic boolean function are related to modified versions of its associated adjacency matrix

on time optimal control of fractional order systems abstract fractional optimal control problem is treated from convex analytical viewpoint sufficient conditions for time optimal control similar to that of pontryagin s maximum principle are obtained for fractional order systems in the sense of riemann liouville and caputo theoretical results are supported by examples

complete characterization of generalized bent and 2 k bent boolean functions in this paper we investigate properties of generalized bent boolean functions and 2 k bent i e negabent octabent hexadecabent et al boolean functions in a uniform framework from the hadamard matrices hod ic and pasalic presented sufficient conditions for generalized bent functions using cyclotomic fields and the decomposition of generalized bent functions we generalize their results prove that hod ic and pasalic s conditions of generalized bent functions are not only sufficient but also necessary and completely characterize generalized bent functions in terms of their component functions furthermore we present a secondary construction of bent functions or semi bent functions from generalized bent functions finally we give the relations of generalized bent functions and 2 k bent functions demonstrate that 2 k bent functions are actually a special class of generalized bent functions and completely characterize 2 k bent functions

fractional variational calculus with classical and combined caputo derivatives abstract we give a proper fractional extension of the classical calculus of variations by considering variational functionals with a lagrangian depending on a combined caputo fractional derivative and the classical derivative euler lagrange equations to the basic and isoperimetric problems as well as transversality conditions are proved

on weak and strong 2 k bent boolean functions in this paper we introduce a sequence of discrete fourier transforms and define new versions of bent functions which we shall call weak and strong octa hexadeca and in general 2 k bent functions we investigate relationships between these classes and completely characterize the octabent and hexadecabent functions in terms of bent functions we further find relative difference sets based upon these functions

on the approximate controllability of semilinear fractional differential systems fractional differential equations have wide applications in science and engineering in this paper we consider a class of control systems governed by the semilinear fractional differential equations in hilbert spaces by using the semigroup theory the fractional power theory and fixed point strategy a new set of sufficient conditions are formulated which guarantees the approximate controllability of semilinear fractional differential systems the results are established under the assumption that the associated linear system is approximately controllable further we extend the result to study the approximate controllability of fractional systems with nonlocal conditions an example is provided to illustrate the application of the obtained theory

approximate controllability of fractional delay dynamic inclusions with nonlocal control conditions we introduce a nonlocal control condition and the notion of approximate controllability for fractional order quasilinear control inclusions approximate controllability of a fractional control nonlocal delay quasilinear functional differential inclusion in a hilbert space is studied the results are obtained by using the fractional power of operators multi valued analysis and sadovskii s fixed point theorem main result gives an appropriate set of sufficient conditions for the considered system to be approximately controllable as an example a fractional partial nonlocal control functional differential inclusion is considered

analysis and numerical approximation of tempered fractional calculus of variations problems abstract in this paper we study variational problems where the cost functional involves the tempered caputo fractional derivative several important optimization conditions are derived to find the optimal solution sufficient and necessary conditions are presented for different variational problems for example the cases of integral isoperimetric problem and holonomic constraints are considered as well as problems with high order derivatives a numerical scheme is proposed to determine approximations of the solution and it is illustrated through some examples

fractional embedding of differential operators and lagrangian systems this paper is a contribution to the general program of embedding theories of dynamical systems following our previous work on the stochastic embedding theory developed with darses c r acad sci ser i math 342 333 2006 preprint ihes 06 27 p 87 2006 we define the fractional embedding of differential operators and ordinary differential equations we construct an operator combining in a symmetric way the left and right riemann liouville fractional derivatives for lagrangian systems our method provides a fractional euler lagrange equation we prove developing the corresponding fractional calculus of variations that such equation can be derived via a fractional least action principle we then obtain naturally a fractional noether theorem and a fractional hamiltonian formulation of fractional lagrangian systems all these constructions are coherents i e the embedding procedure is compatible with the fractional calculus of variations we then extend our results to cover the ostrogradski

generalized fractional calculus with applications to the calculus of variations we study operators that are generalizations of the classical riemann liouville fractional integral and of the riemann liouville and caputo fractional derivatives a useful formula relating the generalized fractional derivatives is proved as well as three relations of fractional integration by parts that change the parameter set of the given operator into its dual such results are explored in the context of dynamic optimization by considering problems of the calculus of variations with general fractional operators necessary optimality conditions of euler lagrange type and natural boundary conditions for unconstrained and constrained problems are investigated interesting results are obtained even in the particular case when the generalized operators are reduced to be the standard fractional derivatives in the sense of riemann liouville or caputo as an application we provide a class of variational problems with an arbitrary kernel that give answer to the important coherence embedding problem illustrative optimization problems are considered

stationarity conservation laws for fractional differential equations with variable coefficients in this paper we study linear fractional differential equations with variable coefficients it is shown that by assuming some conditions for the coefficients the stationarity conservation laws can be derived the area where these are valid is restricted by the asymptotic properties of solutions of the respective equation applications of the proposed procedure include the fractional fokker planck equation in 1 1 and d 1 dimensional space and the fractional klein kramers equation

covariate shift adaptation by importance weighted cross validation a common assumption in supervised learning is that the input points in the training set follow the same probability distribution as the input points that will be given in the future test phase however this assumption is not satisfied for example when the outside of the training region is extrapolated the situation where the training input points and test input points follow different distributions while the conditional distribution of output values given input points is unchanged is called the covariate shift under the covariate shift standard model selection techniques such as cross validation do not work as desired since its unbiasedness is no longer maintained in this paper we propose a new method called importance weighted cross validation iwcv for which we prove its unbiasedness even under the covariate shift the iwcv procedure is the only one that can be applied for unbiased classification under covariate shift whereas alternatives to iwcv exist for regression the usefulness of our proposed method is illustrated by simulations and furthermore demonstrated in the brain computer interface where strong non stationarity effects can be seen between training and test sessions

controllability for a class of fractional order neutral evolution control systems abstract in this paper we consider a class of fractional neutral control systems governed by abstract nonlinear fractional neutral differential equations this paper deals with the exact controllability for fractional differential neutral control systems first we establish a new set of sufficient conditions for the controllability of nonlinear fractional systems by using a fixed point analysis approach further we extend the result to study the controllability concept with nonlocal conditions in particular the controllability of nonlinear systems is established under the natural assumption that the associated linear control system is exactly controllable

solution of the fractional langevin equation and the mittag leffler functions we introduce the fractional generalized langevin equation in the absence of a deterministic field with two deterministic conditions for a particle with unitary mass i e an initial condition and an initial velocity are considered for a particular correlation function that characterizes the physical process and using the methodology of the laplace transform we obtain the solution in terms of the three parameter mittag leffler function as particular cases some recent results are also presented

nonconservative lagrangian and hamiltonian mechanics traditional lagrangian and hamiltonian mechanics cannot be used with nonconservative forces such as friction a method is proposed that uses a lagrangian containing derivatives of fractional order a direct calculation gives an euler lagrange equation of motion for nonconservative forces conjugate momenta are defined and hamilton s equations are derived using generalized classical mechanics with fractional and higher order derivatives the method is applied to the case of a classical frictional force proportional to velocity textcopyright 1996 the american physical society

numerical solution of fractional oscillator equation abstract we focus on a numerical scheme applied for a fractional oscillator equation in a finite time interval this type of equation includes a complex form of left and right sided fractional derivatives its analytical solution is represented by a series of left and right fractional integrals and therefore is difficult in practical calculations here we elaborated two numerical schemes being dependent on a fractional order of the equation the results of numerical calculations are compared with analytical solutions then we illustrate convergence and stability of our schemes

a new method of dynamical stability i e fractional generalized hamiltonian method and its applications fractional generalized hamiltonian method of dynamical stability is presented six criterions for the new method of dynamical stability are given the new method s applications are studied five kinds of actual fractional dynamical models are constructed dynamical stability of the five actual fractional dynamical models is explored in the paper we present fractional generalized hamiltonian method of dynamical stability in terms of riesz riemann liouville derivative and study its applications for an actual dynamical system the fractional generalized hamiltonian method of constructing a fractional dynamical model is given and then the six criterions for fractional generalized hamiltonian method of dynamical stability are presented as applications by using the fractional generalized hamiltonian method we construct five kinds of actual fractional dynamical models which include a fractional euler poinsot model of rigid body that rotates with respect to a fixed point a fractional hojman urrutia model a fractional lorentz dirac model a fractional whittaker model and a fractional robbins lorenz model and we explore the dynamical stability of these models respectively this work provides a general method for studying the dynamical stability of an actual fractional dynamical system that is related to science and engineering

domain adaptation via transfer component analysis domain adaptation allows knowledge from a source domain to be transferred to a different but related target domain intuitively discovering a good feature representation across domains is crucial in this paper we first propose to find such a representation through a new learning method transfer component analysis tca for domain adaptation tca tries to learn some transfer components across domains in a reproducing kernel hilbert space using maximum mean miscrepancy in the subspace spanned by these transfer components data properties are preserved and data distributions in different domains are close to each other as a result with the new representations in this subspace we can apply standard machine learning methods to train classifiers or regression models in the source domain for use in the target domain furthermore in order to uncover the knowledge hidden in the relations between the data labels from the source and target domains we extend tca in a semisupervised learning setting which encodes label information into transfer components learning we call this extension semisupervised tca the main contribution of our work is that we propose a novel dimensionality reduction framework for reducing the distance between domains in a latent space for domain adaptation we propose both unsupervised and semisupervised feature extraction approaches which can dramatically reduce the distance between domain distributions by projecting data onto the learned transfer components finally our approach can handle large datasets and naturally lead to out of sample generalization the effectiveness and efficiency of our approach are verified by experiments on five toy datasets and two real world applications cross domain indoor wifi localization and cross domain text classification