optimal discretization of inverse problems in hilbert scales regularization and self regularization of projection methods we study the efficiency of the approximate solution of ill posed problems based on discretized noisy observations which we assume to be given beforehand a basic purpose of the paper is the consideration of stochastic noise but deterministic noise is also briefly discussed we restrict ourselves to problems which can be formulated in hilbert scales within this framework we shall quantify the degree of ill posedness provide general conditions on projection schemes to achieve the best possible order of accuracy we pay particular attention on the problem of self regularization vs tikhonov regularization moreover we study the information complexity asymptotically any method which achieves the best possible order of accuracy must use at least such amount of noisy observations

solution of a system of nonlinear equations by adomian decomposition method in this paper the adomian decomposition method is applied to solve a system of nonlinear equations convergence of the method is proved and some examples are presented to illustrate the method

irrelevant interactions without composite operators a remark on the universality of second order phase transitions we study the critical behaviour of symmetric 44 theory including irrelevant terms of the form 4 2n 02n in the bare action where 0 is the uv cutoff corresponding e g to the inverse lattice spacing for a spin system the main technical tool is renormalization theory based on the flow equations of the renormalization group which permits us to establish the required convergence statements in generality and rigour as a consequence the effect of irrelevant terms on the critical behaviour may be studied to any order without using renormalization theory for composite operators this is a technical simplification and seems preferable from the physical point of view in this short paper we restrict ourselves for simplicity to the symmetry class of the ising model i e one component 44 theory the method is general however

adomian decomposition a tool for solving a system of fractional differential equations abstract adomian decomposition method has been employed to obtain solutions of a system of fractional differential equations convergence of the method has been discussed with some illustrative examples in particular for the initial value problem d 1 y 1 d n y n t a y 1 y n t y i 0 c i i 1 n where a a i j is a real square matrix the solution turns out to be y x e 1 n 1 x 1 a 1 x n a n y 0 where e 1 n 1 denotes multivariate mittag leffler function defined for matrix arguments and a i is the matrix having ith row as a i 1 a i n and all other entries are zero fractional oscillation and bagley torvik equations are solved as illustrative examples

the fekete szego problem for k uniformly convex functions and for a class defined by the owa srivastava operator abstract by making use of a fractional differential operator due to owa and srivastava a subclass of analytic functions related to k uniformly convex functions is introduced for this class and in particular for the class of k uniformly convex functions the fekete szego problem is completely solved

revised adomian decomposition method for solving a system of nonlinear equations a modification of adomian decomposition method is suggested and used for solving a system of nonlinear equations which yields a series solution with accelerated convergence illustrative examples have been presented to demonstrate the method and the results obtained are compared with those derived from the standard adomian decomposition method

asymptotic behavior of the singular values of a generalization of the operator fractional integration abstract in this paper we find the first term in the asymptotics of singular values of the generalized fractional integration operator

solution of a system of volterra integral equations of the first kind by adomian method in this article we consider linear and non linear systems of integral equations of the first kind the problem of existence and uniqueness are considered the adomian decomposition method is being used to solve these linear and non linear systems of volterra integral equations of the first kind some examples are prepared to show the efficiency and simplicity of the method

new iterative method application to partial differential equations abstract in the present article we implement the new iterative method nim proposed by daftardar gejji and jafari v daftardar gejji h jafari an iterative method for solving non linear functional equations j math anal appl 316 2006 753 763 to solve linear nonlinear partial differential equations of integer and fractional order the results obtained are compared with those obtained by other iterative methods such as adomian decomposition homotopy perturbation and variational iteration methods

solution of the system of ordinary differential equations by adomian decomposition method in this article we use adomian decomposition method which is a well known method for solving functional equations now a days to solve systems of differential equations of the first order and an ordinary differential equation of any order by converting it into a system of differential of the order one theoretical considerations are being discussed and convergence of the method for theses systems is addressed some examples are presented to show the ability of the method for linear and non linear systems of differential equations

a class of analytic functions defined by fractional derivation abstract let z z be analytic in the unit disc z q 2 z d z z where d z z denotes the fractional derivative of z the function z is said to be in r if it satisfies the condition re q z 0 z u r r u and study some subordination properties we also obtain distortion theorems and a coefficient inequality for r finally we discuss the hadamard product of the class r

sharp bounds for singular values of fractional integral operators abstract from the results of dostanic m r dostanic asymptotic behavior of the singular values of fractional integral operators j math anal appl 175 1993 380 391 and v and gorenflo kim tuan v r gorenflo singular values of fractional and volterra integral operators in inverse problems and applications to geophysics industry medicine and technology ho chi minh city 1995 ho chi minh city math soc ho chi minh city 1995 pp 174 185 it is known that the jth singular value of the fractional integral operator of order 0 is approximately j for all large j in this note we refine this result by obtaining sharp bounds for the singular values and use these bounds to show that the jth singular value is j 1 o j 1

a new predictor corrector method for fractional differential equations we present a new predictor corrector method to solve non linear fractional differential equations involving caputo derivative the proposed method is compared with the fractional adams method numerous illustrative examples discussed here demonstrate that the new method is more accurate and time efficient a detailed error analysis given points to the higher accuracy of the new method furthermore the proposed method when applied to fractional analog of chaotic system introduced by bhalekar and daftardar gejji unravels the underlying rich dynamics of the system

asymptotic behavior of the singular values of fractional integral operators in this paper we find the precise asympotic of the singular numbers of the fractional integral operator i x0 x y 1 dy in the case 0 1 2 and improve the known estimates for 1 2 1 also we obtain some results concerning the precise asympotic of the singular numbers of convolution operators similar to the fractional integral operators

applications of fractional calculus to parabolic starlike and uniformly convex functions let a be the class of analytic functions in the open unit disk u given 0 1 let be the operator defined on a by f z 2 z d zf z where d zf is the fractional derivative of f of order a function f in a is said to be in the class sp if f is a parabolic starlike function in this paper several basic properties and characteristics of the class sp are investigated these include subordination inclusion and growth theorems class preserving operators fekete szeg problems and sharp estimates for the first few coefficients of the inverse function

the fekete szego problem for subclasses of analytic functions defined by a differential operator related to conic domains by using a linear multiplier fractional differential operator a new subclass of analytic functions generalized b uniformly convex functions denoted by b sp l m n a c is introduced for this class the fekete szego problem is completely solved various known or new special cases of our results are also pointed out

the time delay restraining the herd behavior with bayesian approach abstract we explore the herd behavior of stock prices influenced by the time delay in a finance system with the delayed heston model on the basis of a bayesian approach for delayed heston model that we proposed and parameter bayesian estimation we simulate the absolute deviation between mean residence time of positive and negative returns to characterize the herd behavior in the plots of absolute deviation against the mean reversion long run variance of volatility or cross correlation between two wiener processes of stock price and volatility the results demonstrate an increasing phenomenon of herd behavior with increasing delay time in the plot of absolute deviation against the amplitude of volatility fluctuations the result indicates an optimal delay time matching minimum herd behavior i e the time delay restrains the herd behavior also the optimal mean reversion long run variance of volatility and cross correlation concerning minimum herd behavior can be observed

fractional bloch equation with delay in this paper we investigate a fractional generalization of the bloch equation that includes both fractional derivatives and time delays the appearance of the fractional derivative on the left side of the bloch equation encodes a degree of system memory in the dynamic model for magnetization the introduction of a time delay on the right side of the equation balances the equation by also adding a degree of system memory on the right side of the equation the analysis of this system shows different stability behavior for the t 1 and the t 2 relaxation processes the t 1 decay is stable for the range of delays tested 1 100 ms while the t 2 relaxation in this model exhibited a critical delay typically 6 ms above which the system was unstable delays are expected to appear in nmr systems in both the system model and in the signal excitation and detection processes therefore by including both the fractional derivative and finite time delays in the bloch equation we believe that we have established a more complete and more realistic model for nmr resonance and relaxation

some numerical methods for solving nonlinear equations by using decomposition technique in this paper we use the system of coupled equations involving an auxiliary function together with decomposition technique to suggest and analyze some new classes of iterative methods for solving nonlinear equations these new methods include the halley method and its variant forms as special cases various numerical examples are given to illustrate the efficiency and performance of the new methods these new iterative methods may be viewed as an addition and generalization of the existing methods for solving nonlinear equations

a new iterative technique for a fractional model of nonlinear zakharov kuznetsov equations via sumudu transform abstract the main objective of this paper is to suggest a new computational technique namely new iterative sumudu transform method nistm to solve numerically nonlinear time fractional zakharov kuznetsov fzk equation in two dimensions we implemented the proposed technique on two test examples plotted the solution and compared the absolute error with the variational iterative technique vim and homotopy perturbation transform method hptm

analysis of nonlinear dynamics and chaos in a fractional order financial system with time delay in this paper a delayed fractional order financial system is proposed and the complex dynamical behaviors of such a system are discussed by numerical simulations a great variety of interesting dynamical behaviors of such a system including single periodic multiple periodic and chaotic motions are displayed in particular the effect of time delay on the chaotic behavior is investigated it is found that an approximate time delay can enhance or suppress the emergence of chaos meanwhile corresponding to different values of delay the lowest orders for chaos to exist in the delayed fractional order financial systems are determined respectively

a coefficient inequality for a subclass of the caratheodory functions defined using conical domains for 0 k k 2 u 1 2 v 2 u 0 let q k z be the riemann map of u z c z 0 let p q k be the class of analytic functions h z subordinate in u to q k z and represented by h z 1 b 1z b 2z 2 z u sharp estimates for b 2 ub 1 2

on classes of analytic functions related to conic domains abstract we introduce classes of analytic functions related to conic domains using a new linear multiplier fractional differential operator d n n n 0 0 1 0 1 0 which is defined as d 0 f z f z d 1 f z 1 f z z f z d f z d 2 f z d d 1 f z d n f z d d n 1 f z where f z 2 z d z f z and d z is the known fractional derivative basic properties of these classes are studied such as inclusion relations and coefficient bounds various known or new special cases of our results are also pointed out

generalized hypergeometric functions associated with k uniformly convex functions abstract for a certain linear operator which is defined by means of the hadamard product or convolution with a generalized hypergeometric function the authors aim at investigating various mapping and inclusion properties involving such subclasses of analytic and univalent functions as for example k uniformly convex functions and k starlike functions relevant connections of the definitions and results presented in this paper with those in several earlier works on the subject are also pointed out

iterative methods with fourth order convergence for nonlinear equations in this paper we suggest and analyze a new three step iterative method for solving nonlinear equations involving only first derive of the function using a new decomposition technique which is due to noor m aslam noor numerical analysis and optimization lecture notes comsats institute of information technology islamabad pakistan 2006 m aslam noor new iterative schemes for nonlinear equations appl math comput in press and noor and noor m aslam noor k inayat noor some iterative schemes for nonlinear equations appl math comput in press we show that this new iterative method has fourth order convergence several numerical examples are given to illustrate the efficiency and performance of the new method

some fractional differintegral equations recently nishimoto j college engrg nihon univ ser b 24 1983 7 13 studied a certain fractional integral equation and a system of simultaneous differintegral equations each of order 12 motivated by nishimoto s work owa and nishimoto j college engrg nihon univ ser b 24 1983 67 72 considered a general fractional differintegral equation the object of the present paper is to investigate some interesting properties of functions which satisfy the general fractional differintegral equation solved by owa and nishimoto

perturbative renormalization of massless φ 4 4 with flow equations perturbative renormalizability proofs in the wilson polchinski renormalization group framework based on flow equations were so far restricted to massive theories here we extend them to euclidean massless 4 4 as a by product of the proof we obtain bounds on the singularity of the green functions at exceptional momenta in terms of the exceptionality of the latter these bounds seem to be new and are quite sharp

he s fractional derivative a powerful tool to fractional fornberg whitham equation abstract in this paper fractional fornberg whitham equation is studied in a fractal process based on he s fractional derivative the fractional complex transform is used to convert the studied fractional equation into an ordinary differential equation and gejji jafari iteration method is used to solve the equation

subordination results for classes of analytic functions related to conic domains defined by a fractional operator abstract let a fractional operator d n n n 0 0 1 2 0 1 0 be defined by d 0 0 f z d 1 f z 1 f z z f z d f z d 2 f z d d 1 f z d n f z d d n 1 f z where f z 2 z d z f z and d z is the known fractional derivative in this paper several interesting subordination results are derived for certain classes of analytic functions related to conic domains defined by the operator d n which yield sharp distortion rotation theorems and koebe domain these results extended corresponding previously known results

picard iteration algorithm combined with gauss seidel technique for initial value problems abstract in this paper we introduce and implement a relatively new improvement for the well known picard s method for studying linear and nonlinear systems of ordinary differential equations in this method the solution takes the form of a rapidly convergent series with easily computable components a mathematica computer algebra system mathematica 5 1 is used to introduce a code which generates the series different illustrative examples have been considered as well as different comparison criterion between the proposed method and modern reliable and conventional methods the deeply mathematical roots of the method fixed point theorem and the correspondence with the theory of algebraic systems makes it is very interesting theoretical considerations are being discussed and convergence of the method is addressed other extensions and applications for further work are mentioned

a certain fractional derivative operator and its applications to a new class of analytic and multivalent functions with negative coefficients recently the authors made use of a certain operator of fractional derivatives in order to introduce and initiate a systematic study of a novel subclass tp of analytic and p valent functions with negative coefficients in this sequel to the aforementioned work they prove a number of closure and inclusion theorems and determine the radii of p valently close to convexity starlikeness and convexity for the class tp they also obtain a class preserving integral operator of the form f z j p z pz z0t 1 t dt p for the class studied here

certain sufficient conditions for a subclass of analytic functions involving hohlov operator making use of the hohlov operator the authors obtain inclusion relations between the classes of certain normalized analytic functions relevant connections of our work with the earlier works are pointed out

chaos in fractional order financial delay system abstract chaotic dynamics of the fractional order financial system involving time delay is studied the numerical simulations are done using the new predictor corrector method proposed by daftardar gejji et al and by modified fractional adams method fam the results obtained using new predictor corrector method are matching with fam it is observed that the new predictor corrector method is more time efficient than the fam

an iterative method for solving nonlinear functional equations an iterative method for solving nonlinear functional equations viz nonlinear volterra integral equations algebraic equations and systems of ordinary differential equation nonlinear algebraic equations and fractional differential equations has been discussed

a reliable modification of adomian decomposition method in this paper we propose a powerful modification of adomian decomposition method that will accelerate the rapid convergence of the series solution the validity of the modified technique is verified through illustrative examples in all cases of differential and integral equations we obtained excellent performance from the modified algorithm the modification could lead to a promising approach for many applications in applied sciences

the modified decomposition method for solving nonlinear algebraic equations in this paper an algorithm based on adomian s decomposition method is developed to approximate the solution of nonlinear algebraic equations the conditions of the convergence which depend on the coefficients of the equation are found the truncation error of the method is obtained special cases of the nonlinear algebraic equation are solved using the modified algorithm the presented work shows that the modified approach gives improvements over existing techniques

solving a system of nonlinear fractional differential equations using adomian decomposition adomian decomposition method has been employed to obtain solutions of a system of nonlinear fractional differential equations dxiyi x ni x y1 yn yi k 0 cki 0 k i 1 i n and dxi denotes caputo fractional derivative some examples are solved as illustrations using symbolic computation

perturbative renormalization of composite operators via flow equations i we apply the general framework of the continuous renormalization group whose significance for perturbative quantum field theories was recognized by polchinski to investigate by new and mathematically simple methods the perturbative renormalization of composite operators in this paper we demonstrate the perturbative renormalizability of the green functions of the euclidean massive 44 theory with one insertion of a possibly oversubtracted in the bphz language composite operator moreover we show that our method admits an easy proof of the zimmermann identities and of the lowenstein rule