The approximate solutions of the time fractional advection-dispersion equation are presented in this article. nonlocal nature solute movement and nonuniformity fluid flow velocity process lead to formation a heterogeneous system, which can be modeled using equation, generalizes classical replaces derivative with Caputo derivative. Researchers use variety numerical techniques study such models, ...

In this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. The homotopy analysis method (HAM) is used for solving this equation. Several examples are given to reconfirm the efficiency of these algorithms. The results of applying this procedure...

We define a theory of Goodwillie calculus for enriched functors from finite pointed simplicial G-sets to symmetric G-spectra, where G is a finite group. We extend a notion of G-linearity suggested by Blumberg to define stably excisive and ρ-analytic homotopy functors, as well as a G-differential, in this equivariant context. A main result of the paper is that analytic functors with trivial deri...

This paper provides both analytical and numerical solutions of (PDEs) involving time-fractional derivatives. We implemented three powerful techniques, including the modified variational iteration technique, Adomian decomposition homotopy analysis to obtain an approximate solution for bounded space variable ν. The Laplace transformation is used in derivative operator enhance proposed methods’ pe...

We use Chen iterated line integrals to construct a topological algebra Ap of separating functions on the Group of Loops LMp. Ap has an Hopf algebra structure which allows the construction of a group structure on its spectrum. We call this topological group, the group of generalized loops L̃Mp. Then we develope a Loop Calculus, based on the Endpoint and Area Derivative Operators, providing a rigo...

A new homotopy perturbation method (NHPM) is applied to system of variable coefficient coupled Burgers' equation with time-fractional derivative. The fractional derivatives are described in the Caputo fractional derivative sense. The concept of new algorithm is introduced briefly, and NHPM is examined for two systems of nonlinear Burgers' equation. In this approach, the solution is considered a...

In this work, we present a semi-analytical technique to find an approximate result of the conformable fractional partial differential equations (CFPDEs). The order derivative will be in (CFD) sense. This definition is effective and simple solution that have intricate with classical like Riemann-Liouville Caputo. Furthermore, obtained by proposed those previous studies used other types methods (...

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