‎in this paper, we discuss about existence of solution forintegro-differential system and then we solve it  by using the petrov-galerkin method. in the petrov-galerkin method choosing the trial and test space is important, so  we use alpert multi-wavelet as basisfunctions for these spaces. orthonormality is one of theproperties of alpert multi-wavelet which helps us to reducecomputations in the...

This study develops and analyzes preconditioned Krylov subspace methods to solve linear systems arising from discretization of the time-independent space-fractional models. First, we apply shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we employee two preconditioned iterative methods, namely, the preconditioned gen...

In this work, we proposed an effective method based on cubic and pantic B-spline scaling functions to solve partial differential equations of fractional order. Our method is based on dual functions of B-spline scaling functions. We derived the operational matrix of fractional integration of cubic and pantic B-spline scaling functions and used them to transform the mentioned equations to a syste...

S-asymptotically ω-periodic functions have applications to several problems, for example in the theory of functional differential equations, fractional differential equations, integral equations and partial differential equations. The concept of S-asymptotic ω-periodicity was introduced in the literature by Henrı́quez et al. 1, 2 . Since then, it attracted the attention of many researchers see 1...

In this study, solutions of time-space fractional partial differential equations(FPDEs) are obtained by utilizing the Shehu transform iterative method. The utilityof technique is shown getting numerical to a large number FPDEs.

In this research work, the numerical scheme for obtaining linear time-fractional differential equations was considered and nature of these are in sense Caputo. A theorem proved to show Kamal transform \(n\)th order Caputo derivatives. Finally, three problems were regarding which presented that convergence provided high accuracy solving fractional equations.

This paper shows how to use the fractional Sumudu homotopy perturbation technique (SHP) with Caputo operator (CF) solve time linear and nonlinear partial differential equations. The transform (ST) (HP) are combined in this approach. In definition, derivative is defined. general, method straightforward execute yields good results. There some examples offered demonstrate technique's validity use.