In this paper, by introducing the fractional derivative in the sense of Caputo, the Adomian decomposition method is directly extended to study the coupled Burgers equations with timeand space-fractional derivatives. As a result, the realistic numerical solutions are obtained in a form of rapidly convergent series with easily computable components. The figures show the effectiveness and good acc...

In this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann–Liouville) or a solution with increasing...

This article deals with the determination of the fractional rate of convergence to the unit of some neural network operators, namely, the CardaliaguetEuvrard and ”squashing” operators. This is given through the moduli of continuity of the involved right and left Caputo fractional derivatives of the approximated function and they appear in the right-hand side of the associated Jackson type inequ...

Based on He's variational iteration method idea, we modified the fractional variational iteration method and applied it to construct some approximate solutions of the generalized time-space fractional Schrödinger equation (GFNLS). The fractional derivatives are described in the sense of Caputo. With the help of symbolic computation, some approximate solutions and their iterative structure of th...

A fractional order HIV model with both virus-tocell and cell-to-cell transmissions and therapy effect is investigated. The conditions for the existence of the equilibria are determined. Local stability analysis of the HIV model is studied by using the fractional Routh-Hurwitz stability conditions. We have generalized the integer LaSalle’s invariant theorem into fractional system and given some ...

Physical processes with memory and hereditary properties can be best described by fractional differential equations based on the memory effect of fractional derivatives. For that reason reliable and efficient techniques for the solution of fractional differential equations are needed. Our aim is to generalize the wavelet collocation method to fractional partial differential equations using cubi...

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.

The aim of this paper is to present a new numerical method for solving the Bagley-Torvik equation. This equation has an important role in fractional calculus. The fractional derivatives are described based on the Caputo sense. Some properties of the sinc functions required for our subsequent development are given and are utilized to reduce the computation of solution of the Bagley-Torvik equati...

This survey is devoted to some fractional extensions of the incomplete lumped formulation, the lumped formulation and the formulation of Lauwerier of the temperature field problem in oil strata. The method of integral transforms is used to solve the corresponding boundary value problems for the fractional heat equation. By using Caputo’s differintegration operator and the Laplace transform, new...