a numerical method for an integro differential equation with memory in banach spaces qualitative properties a first order method is considered for the discretization in time of an integro differential equation which can be written as d alpha u t a u t f t 1 alpha 2 where a d a subset x to x is a sectorial operator in a banach space x qualitative properties of the numerical solution such as contractivity and positivity are studied a numerical illustration is provided

fractional high order methods for the nonlinear fractional ordinary differential equation abstract in this paper we consider the nonlinear fractional order ordinary differential equation 0 d t y t f y t t 0 n 1 n y i 0 y 0 i i 0 1 2 n 1 where f y t satisfies the l condition i e f y 1 t f y 2 t l y 1 y 2 in t 0 t fractional order linear multiple step methods are introduced the high order 2 6 approximations of the fractional order ordinary differential equation with an initial value are proposed the consistence convergence and stability of the fractional high order methods are proved finally some numerical examples are provided to show that the fractional high order methods for solving the fractional order nonlinear ordinary differential equation are computationally efficient solution methods

cauchy problems for fractional differential equations with riemann liouville fractional derivatives abstract in this paper we are concerned with cauchy problems of fractional differential equations with riemann liouville fractional derivatives in infinite dimensional banach spaces we introduce the notion of fractional resolvent obtain some its properties and present a generation theorem for exponentially bounded fractional resolvents moreover we prove that a homogeneous order cauchy problem is well posed if and only if its coefficient operator is the generator of an order fractional resolvent and we give sufficient conditions to guarantee the existence and uniqueness of weak solutions and strong solutions of an inhomogeneous order cauchy problem

gromov witten classes quantum cohomology and enumerative geometry the paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry in particular it contains an axiomatic treatment of gromov witten classes and a discussion of their properties for fano varieties cohomological field theories are defined and it is proved that tree level theories are determined by their correlation functions application to counting rational curves on del pezzo surfaces and projective spaces are given

linear approximation of transfer function with a pole of fractional power two methods for the linear approximation of a transfer function with a pole of fractional power are presented analog circuit models are developed and their frequency response curves and step response curves are compared it was found that the pade method gives a better approximation than wang and hsia s method within the frequency limit as specified

development of the kansa method for solving seepage problems using a new algorithm for the shape parameter optimization abstract in this research the kansa or multiquadric method mq has been developed for solving the seepage problems in 2d and 3d arbitrary domains this research is the first application of this method for seepage analysis in both confined and unconfined porous media the domain decomposition approach has been employed for applying mq method easily in inhomogeneous and irregular complex geometries and decreasing the computational costs for determining the optimum shape parameter that affects strongly the accuracy of mq and other rfb methods a new scheme that decreases drastically the computational time is introduced the efficiency of the proposed algorithm has been examined under various radial basis functions variations of number of interpolating points and points distribution through a numerical example with analytical solution eventually three examples including different boundary conditions are presented comparing results of the examples with other numerical methods indicates that the present approach has high capability and accuracy in solving seepage problems

lagrangian floer superpotentials and crepant resolutions for toric orbifolds we investigate the relationship between the lagrangian floer superpotentials for a toric orbifold and its toric crepant resolutions more specifically we study an open string version of the crepant resolution conjecture crc which states that the lagrangian floer superpotential of a gorenstein toric orbifold mathcal x and that of its toric crepant resolution y coincide after analytic continuation of quantum parameters and a change of variables relating this conjecture with the closed crc we find that the change of variable formula which appears in closed crc can be explained by relations between open orbifold gromov witten invariants we also discover a geometric explanation in terms of virtual counting of stable orbi discs for the specialization of quantum parameters to roots of unity which appears in ruan s original crc gromov witten theory of spin curves and orbifolds contemp math amer math soc providence ri pp 117 126 2006 we prove the open crc for the weighted projective spaces mathcal x mathbb p 1 ldots 1 n using an equality between open and closed orbifold gromov witten invariants along the way we also prove an open mirror theorem for these toric orbifolds

on the obstructed lagrangian floer theory abstract lagrangian floer homology in a general case has been constructed by fukaya oh ohta and ono where they construct an a algebra or an a bimodule from lagrangian submanifolds they developed obstruction and deformation theories of the lagrangian floer homology theory but for obstructed lagrangian submanifolds the standard lagrangian floer homology cannot be defined we explore several well known homology theories on these a objects which are hochschild and cyclic homology for an a objects and chevalley eilenberg or cyclic chevalley eilenberg homology for their underlying l objects we show that these homology theories are well defined and invariant even in the obstructed cases due to the existence of m 0 the standard homological algebra does not work and we develop analogous homological algebra over novikov fields we provide computations of these homology theories in some cases we show that for an obstructed a algebra with a non trivial primary obstruction chevalley eilenberg floer homology vanishes whose proof is inspired by the comparison with cluster homology theory of lagrangian submanifolds by cornea and lalonde in contrast we also provide an example of an obstructed case whose cyclic floer homology is non vanishing

the fractional diffusion equation in one space and in one time dimension a diffusion equation is solved where the first time derivative is replaced by the fractional time derivative 0 1 the solution is given in closed form in terms of fox functions

s asymptotically ω periodic and asymptotically ω periodic solutions to semi linear cauchy problems with non dense domain abstract in this work we study the existence and uniqueness of s asymptotically periodic and asymptotically periodic solutions to a first order differential equation with linear part dominated by a hille yosida operator with non dense domain applications to partial differential equations fractional integro differential and neutral differential equations are given

spectral analysis of fractional kinetic equations with random data we present a spectral representation of the mean square solution of the fractional kinetic equation also known as fractional diffusion equation with random initial condition gaussian and non gaussian limiting distributions of the renormalized solution of the fractional in time and in space kinetic equation are described in terms of multiple stochastic integral representations

stochastic solution of space time fractional diffusion equations classical and anomalous diffusion equations employ integer derivatives fractional derivatives and other pseudodifferential operators in space in this paper we show that replacing the integer time derivative by a fractional derivative subordinates the original stochastic solution to an inverse stable subordinator process whose probability distributions are mittag leffler type this leads to explicit solutions for space time fractional diffusion equations with multiscaling space fractional derivatives and additional insight into the meaning of these equations

the wall crossing formula and lagrangian mutations abstract we prove a general form of the wall crossing formula which relates the disk potentials of monotone lagrangian submanifolds with their floer theoretic behaviour away from a donaldson divisor we define geometric operations called mutations of lagrangian tori in del pezzo surfaces and in toric fano varieties of higher dimension and study the corresponding wall crossing formulas that compute the disk potential of a mutated torus from that of the original one in the case of del pezzo surfaces this justifies the connection between vianna s tori and the theory of mutations of landau ginzburg seeds in higher dimension this provides new lagrangian tori in toric fanos corresponding to different chambers of the mirror variety including ones which are conjecturally separated by infinitely many walls from the chamber containing the standard toric fibre

mild solutions to the time fractional navier stokes equations in r n abstract this paper addresses the existence and uniqueness of mild solutions to the navier stokes equations with time fractional differential operator of order 0 1 several interesting properties about the solution are also highlighted like regularity and decay rate in lebesgue spaces which will depend on the fractional exponent moreover it is shown that the l p exponent range which the solution belongs to is different from the range for the solution of the classical problem with 1

compactness in the adiabatic limit of disk vortices this paper is the first input towards an open analogue of the quantum kirwan map we consider the adiabatic limit of the symplectic vortex equation over the unit disk for a hamiltonian g manifold with lagrangian boundary condition by blowing up the metric on the disk we define an appropriate notion of stable solutions in the limit and prove that any sequence of disk vortices with energy uniformly bounded has a subsequence converging to such a stable object we also proved several analytical properties of vortices over the upper half plane which are new type of bubbles appearing in our compactification

an efficient numerical scheme for burgers equation this paper applies the multiquadric mq as a spatial approximation scheme for solving the nonlinear burgers equation for comparison purposes a low order explicit finite difference approximation of the time derivative is employed by decreasing the time step of the computation it is shown that the major numerical error is from the time integration instead of the mq spatial approximation the numerical results indicate that this mq offers an excellent approximation for all possible values of reynolds number an adaptive algorithm is also developed to adjust the mq interpolation points to the peak of the shock wave which is shown to provide an improved numerical result numerical comparisons are made with most of the existing numerical schemes for solving the burgers equation

piecewise polynomial collocation for linear boundary value problems of fractional differential equations we consider a class of boundary value problems for linear multi term fractional differential equations which involve caputo type fractional derivatives using an integral equation reformulation of the boundary value problem some regularity properties of the exact solution are derived based on these properties the numerical solution of boundary value problems by piecewise polynomial collocation methods is discussed in particular we study the attainable order of convergence of proposed algorithms and show how the convergence rate depends on the choice of the grid and collocation points theoretical results are verified by two numerical examples

a unification theory of krasnoselskii for differential equations abstract the theory of differential equations is very broad and contains many seemingly unrelated types of problems with markedly different methods of solution it is very difficult to discern any unity in the theory yet sixty years ago one of the foremost investigators krasnoselskii suggested the possibility of finding unity he claimed that the inversion of a perturbed differential operator yields the sum of a contraction and compact map accordingly he proved a general fixed point theorem to cover this situation in this paper we begin a long study with a view to putting his idea to the test we begin with fractional differential equations of caputo type continue to neutral functional differential equations and conclude with a study of an old problem of volterra which continues to describe many important real world problems for these problems there is the perfect unity predicted by krasnoselskii it is an invitation to continue the study by examining other important real world problems

unique continuation property for multi terms time fractional diffusion equations this paper concens about a carleman estimate which can give the unique continuation property of solutions for a multi terms time fractional diffusion equation up to order alpha 0 alpha 2 with general time dependent second order strongly elliptic operator for the diffusion by using a special holmgren type transformation which is linear with respect to time the estimate giving a local unique continuation of solutions is derived via some subelliptic estimate for an operator associated to this transformed equation using calculus of pseudo differential operators after that we have given a new argument to derive the global unique continuation of solutions here the global unique continuation means as follows if u is a solution of the multi terms time fractional diffusion equation in a domain over the time interval 0 t and it is supported on t ge 0 then a zero set of solution over a subdomain of omega can be continued to 0 t times omega

cauchy problem for fractional diffusion equations abstract we consider an evolution equation with the regularized fractional derivative of an order 0 1 with respect to the time variable and a uniformly elliptic operator with variable coefficients acting in the spatial variables such equations describe diffusion on inhomogeneous fractals a fundamental solution of the cauchy problem is constructed and investigated

on s asymptotically ω periodic functions and applications abstract let x be a banach space and r a bounded function u c 0 x is called s asymptotically periodic if lim t u t u t 0 in this paper we establish conditions under which an s asymptotically periodic function is asymptotically periodic and we discuss the existence of s asymptotically periodic and asymptotically periodic solutions for an abstract integral equation some applications to partial differential equations and partial integro differential equations are considered

waveform relaxation methods for fractional differential equations with the caputo derivatives in this paper we report new waveform relaxation methods for fractional differential equations with the caputo derivatives the convergence properties of the waveform relaxation methods are studied under linear and nonlinear conditions for the right hand side of equations some convergent splittings are given this is the first time for studying the waveform relaxation methods for fractional differential equations in references

existence of s asymptotically ω periodic solutions for fractional order functional integro differential equations with infinite delay abstract we study s asymptotically periodic solutions of the abstract fractional equation u 1 a u f t u t 1 2 where a is a linear operator of sectorial type 0

maximum principle for the multi term time fractional diffusion equations with the riemann liouville fractional derivatives in this paper the initial boundary value problems for linear and non linear multi term fractional diffusion equations with the riemann liouville time fractional derivatives are considered to guarantee the uniqueness of solutions we employ the weak and the strong maximum principles for the equations under consideration that are formulated and proved in this paper for the first time an essential element of our proof of the maximum principles is an estimation for the value of the riemann liouville fractional derivative of a function at its maximum point that is established in this paper for a wider space of functions compared to those used in our previous publications in the linear case the solutions to the problems under consideration are constructed in form of the fourier series with respect to the eigenfunctions of the corresponding eigenvalue problems

on fractional duhamelʼs principle and its applications abstract the classical duhamel principle established nearly 200 years ago by jean marie constant duhamel reduces the cauchy problem for an inhomogeneous partial differential equation to the cauchy problem for the corresponding homogeneous equation in this paper we generalize this famous principle to a wide class of fractional order differential operator equations

a unified theory of radial basis functions native hilbert spaces for radial basis functions ii abstract this contribution provides a new formulation of the theory of radial basis functions in the context of integral operators instead of fourier transforms the most important tools now are expansions into eigenfunctions this unifies the theory of radial basis functions in r d with the theory of zonal functions on the sphere sd 1 and the theory of kernel functions on riemannian manifolds new characterizations of native spaces and positive definite functions are included the paper is a self contained continuation of an earlier survey r schaback international series of numerical mathematics vol 132 birkhauser basel 1999 pp 255 282 over the native spaces associated to not necessarily radial basis functions

error estimate in fractional differential equations using multiquadratic radial basis functions the purpose of this paper is to investigate the collocation method based on multiquadric mq radial basis functions rbfs for fractional differential equations fdes in the process of doing this a scattered data rbf interpolation is considered a posterior error bound for the smooth solutions of fdes in the proposed method is established in the l 2 norm using an alternate characterization of the native space numerical results are presented which confirm the theoretical prediction of the convergence behavior of the proposed method

abstract fractional cauchy problems with almost sectorial operators abstract of concern are the cauchy problems for linear and semilinear time fractional evolution equations involving in the linear part a linear operator a whose resolvent satisfies the estimate of growth 1 0 in a sector of the complex plane which occurs when one considers for instance the partial differential operators in the limit domain of dumb bell with a thin handle or in the space of holder continuous functions by constructing a pair of families of operators in terms of the generalized mittag leffler type functions and the resolvent operators associated with a for the first time and a deep analysis on the properties for these families we obtain the existence and uniqueness of mild solutions and classical solutions to the cauchy problems moreover we present three examples to illustrate the feasibility of our results

homological mirror symmetry for punctured spheres we prove that the wrapped fukaya category of a punctured sphere s with an arbitrary number of points removed is equivalent to the triangulated category of singularities of a mirror landau ginzburg model proving one side of the homological mirror symmetry conjecture in this case by investigating fractional gradings on these categories we conclude that cyclic covers on the symplectic side are mirror to orbifold quotients of the landau ginzburg model

products of floer cohomology of torus fibers in toric fano manifolds we compute the ring structure of floer cohomology groups of lagrangian torus fibers in some toric fano manifolds continuing the study of co related a formulas hold for a transversal choice of chains two different computations are provided a direct calculation using the classification of holomorphic discs by oh and the author in co and another method by using an analogue of divisor equation in gromov witten invariants to the case of discs floer cohomology rings are shown to be isomorphic to clifford algebras whose quadratic forms are given by the hessians of functions w which turn out to be the superpotentials of landau ginzburg mirrors in the case of open image in new window this proves the prediction made by hori kapustin and li by b model calculations via physical arguments the latter method also provides correspondence between higher derivatives of the superpotential of lg mirror with the higher products of the a or l algebra of the lagrangian submanifold

floer cohomology and pencils of quadrics there is a classical relationship in algebraic geometry between a hyperelliptic curve and an associated pencil of quadric hypersurfaces we investigate symplectic aspects of this relationship with a view to applications in low dimensional topology

a de giorgi nash type theorem for time fractional diffusion equations we study the regularity of weak solutions to linear time fractional diffusion equations in divergence form of arbitrary time order alpha in 0 1 the coefficients are merely assumed to be bounded and measurable and they satisfy a uniform parabolicity condition our main result is a de giorgi nash type theorem which gives an interior holder estimate for bounded weak solutions in terms of the data and the l infty bound of the solution the proof relies on new a priori estimates for time fractional problems and uses de giorgi s technique and the method of non local growth lemmas which has been introduced recently in the context of nonlocal elliptic equations involving operators like the fractional laplacian

regularity of mild solutions for a class of fractional order differential equations in this article we show sufficient conditions ensuring the existence and uniqueness of a mild solution to the equation d au t au t d a 1f t u t 1 a 2 email protected r in the same space where f belongs here a is a sectorial operator defined in a banach space x d a is the fractional derivative in the riemann liouville sense and f x email protected x for each email protected x where w x is a vector valued subspace of the space of continuous and bounded functions the subspaces w x that we will consider in this article are the space of periodic almost periodic almost automorphic and compact almost automorphic vector valued functions among others in particular we extend and unify recent results established for the equation in the papers agarwal et al 2010 cuevas et al 2010 and cuevas and lizama 2008

faces and traces of the unit ball of a symmetric gauge function abstract we investigate the faces of the closed unit ball bg x g x 1 of a symmetric gauge function g r n r firstly we describe the group of symmetries of a face f of bg in terms of its barycenter we introduce the concept of standard face of bg i e a face whose relative interior meets the set d x r n x 1 x n 0 called here the standard cone of r n and the concept of trace of a face f which is the intersection of f with d characterizations of standard faces are given and we show that the trace of a face if nonempty is the trace of a standard face it is proved that a face f and its trace have the same dimension iff f is a standard face a relation is found between the dimension of f and the dimension of its symmetry core i e the set of points of f that are fixed by all symmetries of f other results of this type are given the main result has a long and delicate proof it completely characterizes in several different ways the subsets of bg that are traces of faces of bg

on accurate product integration rules for linear fractional differential equations this paper addresses the numerical solution of linear fractional differential equations with a forcing term competitive and highly accurate product integration rules are derived by starting from an equivalent formulation in terms of a volterra integral equation with a generalized mittag leffler function in the kernel the error analysis is reported and aspects related to the computational complexity are treated numerical tests confirming the theoretical findings are presented

on s asymptotically ω periodic functions on banach spaces and applications abstract this paper is devoted to the study of the class of continuous and bounded functions f 0 x for which exists 0 such that lim t f t f t 0 in the sequel called s asymptotically periodic functions we discuss qualitative properties and establish some relationships between this type of functions and the class of asymptotically periodic functions we also study the existence of s asymptotically periodic mild solutions of the first order abstract cauchy problem in banach spaces

asymptotic periodicity for some evolution equations in banach spaces abstract this work deals with the existence and uniqueness of pseudo almost periodic and asymptotically periodic mild solutions to some evolution equations in banach spaces

asymptotic periodicity for hyperbolic evolution equations and applications we study the existence and uniqueness of pseudo s asymptotically periodic mild solutions for hyperbolic evolution equations we show concrete applications of our methods

weighted sp pseudo s asymptotic periodicity and applications to volterra integral equations abstract this paper is related to the function space formed by weighted sp pseudo s asymptotic periodicity and their applications initially the translation invariance and completeness of the function space are investigated additionally the composition theorem and convolution operator generated by lebesgue integrable functions are presented finally existence and uniqueness of solutions with weighted sp pseudo s asymptotic periodicity for two classes of volterra equations are proved by using the results obtained above and some concrete examples are given the methods mainly include minkowski s inequality convolution inequality contraction mapping principle and especially the generalized minkowski s inequality our results extend some known results on asymptotic periodicity

the numerical solution of nonlinear high dimensional generalized benjamin bona mahony burgers equation via the meshless method of radial basis functions in this paper a numerical technique is proposed for solving the nonlinear generalized benjamin bona mahony burgers equation firstly we obtain a time discrete scheme by approximating the first order time derivative via forward finite difference formula then we use kansa s approach to approximate the spatial derivatives we prove that the time discrete scheme is unconditionally stable and convergent in time variable using the energy method also we show that convergence order of the time discrete scheme is o t we solve the two dimensional version of this equation using the method presented in this paper on different geometries such as the rectangular triangular and circular domains and also the three dimensional case is solved on the cubical and spherical domains the aim of this paper is to show that the meshless method based on the radial basis functions and collocation approach is also suitable for the treatment of the nonlinear partial differential equations also several test problems including the three dimensional case are given numerical examples confirm the efficiency of the proposed scheme

asymptotically periodic solutions of fractional differential equations abstract we study the existence of pseudo s asymptotically periodic mild solutions for a class of abstract fractional differential equation

the stability of the unit balls of symmetric and unitarily invariant norms abstract a compact convex set k is called stable if the midpoint mapping k k k x y x y 2 is open the main result asserts that the stability of the closed unit ball of a unitarily invariant norm is equivalent to the stability of the closed unit ball of the associated symmetric gauge function this result as well as other pointwise related results are obtained using a recently found close relationship between the facial structures of those two kinds of unit balls

s asymptotically ω periodic solutions to some classes of partial evolution equations abstract in this paper we give some sufficient conditions for the existence and uniqueness of s asymptotically periodic mild solutions to some classes of partial evolution equations in banach spaces the main result is obtained by means of the banach fixed point principle

time discretization of fractional subdiffusion equations via fractional resolvent operators abstract in this work we study time discretization of subdiffusion equations that is fractional differential equations of order 0 1 assuming that a is the generator of a fractional resolvent family s t t 0 which allows to write the solution to the subdiffusion equation t u t a u t f t as a variation of constants formula we find an interesting connection between s t t 0 and a discrete resolvent family s n n n and then by using the properties of s t t 0 we study the existence of solutions to the discrete subdiffusion equation c u n a u n f n n n where based on the backward euler method for a 0 given c u n is an approximation of t u t at time t n n we study simultaneously the fractional derivative in the caputo and riemann liouville sense we also provide error estimates and some experiments to illustrate the results

l p error estimates for shifted surface spline interpolation on sobolev space the accuracy of interpolation by a radial basis function is usually very satisfactory provided that the approximant f is reasonably smooth however for functions which have smoothness below a certain order associated with the basis function no approximation power has yet been established hence the purpose of this study is to discuss the lp approximation order 1 p of interpolation to functions in the sobolev space wpk with k max 0 d 2 d p we are particularly interested in using the shifted surface spline which actually includes the cases of the multiquadric and the surface spline moreover we show that the accuracy of the interpolation method can be at least doubled when additional smoothness requirements and boundary conditions are met

optimal constant shape parameter for multiquadric based rbf fd method radial basis functions rbfs have become a popular method for interpolation and solution of partial differential equations pdes many types of rbfs used in these problems contain a shape parameter and there is much experimental evidence showing that accuracy strongly depends on the value of this shape parameter in this paper we focus on pde problems solved with a multiquadric based rbf finite difference rbf fd method we propose an efficient algorithm to compute the optimal value of the shape parameter that minimizes the approximation error the algorithm is based on analytical approximations to the local rbf fd error derived in 1 we show through several examples in 1d and 2d both with structured and unstructured nodes that very accurate solutions compared to finite differences can be achieved using the optimal value of the constant shape parameter

the first integral method for some time fractional differential equations abstract in this paper the fractional derivatives in the sense of modified riemann liouville derivative and the first integral method are employed for constructing the exact solutions of nonlinear time fractional partial differential equations the power of this manageable method is presented by applying it to several examples this approach can also be applied to other nonlinear fractional differential equations

maximum principle for the generalized time fractional diffusion equation abstract in the paper a maximum principle for the generalized time fractional diffusion equation over an open bounded domain g 0 t g r n is formulated and proved the proof of the maximum principle is based on an extremum principle for the caputo dzherbashyan fractional derivative that is given in the paper too the maximum principle is then applied to show that the initial boundary value problem for the generalized time fractional diffusion equation possesses at most one classical solution and this solution continuously depends on the initial and boundary conditions

weak solutions to non homogeneous boundary value problems for time fractional diffusion equations abstract we discuss an initial boundary problem for a time fractional diffusion equation with non zero dirichlet boundary values which belong to l 2 in time t and to a sobolev space of negative order in space and prove the unique existence of weak solutions and a priori estimates the proof is based on the caputo fractional derivative in sobolev spaces and the transposition method we show one application to the existence of solution to an optimal control problem

convergence analysis of the jacobi spectral collocation methods for volterra integral equations with a weakly singular kernel in this paper a jacobi collocation spectral method is developed for volterra integral equations of second kind with a weakly singular kernel we use some function transformation and variable transformations to change the equation into a new volterra integral equation deflned on the standard interval i1 1 so that the solution of the new equation possesses better regularity and the jacobi orthogonal polynomial theory can be applied conveniently in order to obtain high order accuracy for the approx imation the integral term in the resulting equation is approximated by using jacobi spectral quadrature rules the convergence analysis of this novel method is based on the lebesgue constants corresponding to the lagrange interpolation polynomials poly nomials approximation theory for orthogonal polynomials and the operator theory the spectral rate of convergence for the proposed method is established in the l 1 norm and weighted l 2 norm numerical results are presented to demonstrate the efiectiveness of the proposed method

on mittag leffler type functions in fractional evolution processes abstract we review a variety of fractional evolution processes so defined being governed by equations of fractional order whose solutions turn out to be related to mittag leffler type functions the chosen equations are the simplest of the fractional calculus and include the abel integral equations of the second kind which are relevant in typical inverse problems and the fractional differential equations which govern generalized relaxation and oscillation phenomena

reconstruction of the temporal component in the source term of a time fractional diffusion equation in this article we consider the reconstruction of in the time fractional diffusion equation by observation at a single point x 0 we are mainly concerned with the situation of which is practically important but has not been well investigated in literature assuming finite sign changes of and an extra observation interval we establish the multiple logarithmic stability for the problem based on a reverse convolution inequality and a lower estimate for positive solutions meanwhile we develop a fixed point iteration for the numerical reconstruction and prove its convergence the performance of the proposed method is illustrated by several numerical examples