We define, in a consistent way, non-local pseudo-differential operators acting on a space of analytic functionals. These operators include the fractional derivative case. In this context we show how to solve homogeneous and inhomogeneous equations associated with these operators. We also extend the formalism to d-dimensional space-time solving, in particular, the fractional Wave and Klein-Gordo...

‎In this paper we propose a method for computing approximations of solution of fuzzy fractional differential equations using fuzzy variational iteration method. Defining a fuzzy fractional derivative, we verify the utility of the method through two illustrative ‎examples.‎

Navier–Stokes (NS) equation, in fluid mechanics, is a partial differential equation that describes the flow of incompressible fluids. We study fractional derivative by using mild solution. In this work, anomaly diffusion fractal media simulated equations (NSEs) with time-fractional derivatives order β∈(0,1). Hγ,℘, we prove existence and uniqueness local global solutions fuzzy techniques. Meanwh...

In this paper, the solution of the evolutionaryfourth-order in space, Sivashinsky equation is obtained by meansof homotopy perturbation method (textbf{HPM}). The results revealthat the method is very effective, convenient  and quite accurateto systems of nonlinear partial differential equations.

Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditi...

This manuscript introduces a discrete technique to estimate the solution of double-fractional two-component Bose–Einstein condensate. The system consists two coupled nonlinear parabolic partial differential equations whose solutions are complex functions, and spatial fractional derivatives interpreted in Riesz sense. Initial homogeneous Dirichlet boundary data imposed on multidimensional domain...