Abstract The Cauchy problem of a time-space fractional partial differential equation which has as particular cases the Klein-Gordon equation, generalized expression heat and two apparently unexplored integro-differential equations in context physics, is proposed solved for delta initial condition. Series H-Fox functions are obtained solution.

This paper reports a new spectral collocation algorithm for solving time-space fractional partial differential equations with subdiffusion and superdiffusion. In this scheme we employ the shifted Legendre Gauss-Lobatto collocation scheme and the shifted Chebyshev Gauss-Radau collocation approximations for spatial and temporal discretizations, respectively. We focus on implementing the new algor...

This paper is devoted to an innovative and efficient technique for solving space–time fractional differential equations (STFPDEs). To this end, we apply the Tau method such that bases used are interpolating scaling functions (ISFs). The operational metrics derivative operator integration introduce matrix Caputo derivative. Due some characteristics of ISFs, as interpolation, computation costs ca...

the complex-step derivative approximation is applied to compute numerical derivatives. in this study, we propose a new formula of fractional complex-step method utilizing jumarie definition. based on this method, we illustrated an approximate analytic solution for the fractional cauchy-euler equations. application in image denoising is imposed by introducing a new fractional mask depending on s...

The paper is concerned with reflecting Brownian motion (RBM) in domains with deterministic moving boundaries, also known as “noncylindrical domains,” and its connections with partial differential equations. Construction is given for RBM in C3-smooth time-dependent domains in the n-dimensional Euclidean space Rn. We present various sample path properties of the process, two-sided estimates for i...

In this letter we develop a new generalization of the two-dimensional differential transform method that will extend the application of the method to linear partial differential equations with spaceand time-fractional derivatives. The new generalization is based on the two-dimensional differential transform method, generalized Taylor’s formula and Caputo fractional derivative. Several illustrat...

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...

In this paper, based on certain variable transformation, we apply the known (G’/G) method to seek exact solutions for three fractional partial differential equations: the space fractional (2+1)-dimensional breaking soliton equations, the space-time fractional Fokas equation, and the spacetime fractional Kaup-Kupershmidt equation. The fractional derivative is defined in the sense of modified Rie...