this paper studies the existence of solutions for acoupled system of nonlinear fractional differential equations. newexistence and uniqueness results are established using banach fixedpoint theorem. other existence results are obtained using schaeferand krasnoselskii fixed point theorems. some illustrative examplesare also presented.

In this paper, we used the natural decomposition approach with non-singular kernel derivatives to find solution nonlinear fractional Gardner and Cahn–Hilliard equations arising in fluid flow. The derivative is considered an Atangana–Baleanu Caputo manner (ABC) Caputo–Fabrizio (CF) throughout paper. We implement transform aid of suggested obtain followed by inverse transform. To show accuracy va...

Present paper deals with the solution of time and space fractional Pennes bioheat equation. We consider time fractional derivative and space fractional derivative in the form of Caputo fractional derivative of order [Formula: see text] and Riesz-Feller fractional derivative of order [Formula: see text] respectively. We obtain solution in terms of Fox's H-function with some special cases, by usi...

The purpose of this article is to solve a nonlinear fractional Klein–Fock–Gordon equation that involves recently created non-singular kernel derivative by Caputo–Fabrizio. Motivated some physical applications related the equation, we focus our study on and phenomena rated it. findings are crucial essential for explaining variety processes. In order find satisfactory approximations offered probl...

The objective of this manuscript is to present a novel approach modeling influenza A disease dynamics by incorporating the Caputo-Fabrizio (CF) fractional derivative operator into model. Particularly distinct contact rates between exposed and infected individuals are taken account in model under study, concept explored with respect component. We demonstrate existence uniqueness solution obtain ...

In this paper, some theorems of the classical power series are generalized for the fractional power series. Some of these theorems are constructed by using Caputo fractional derivatives. Under some constraints, we proved that the Caputo fractional derivative can be expressed in terms of the ordinary derivative. New construction of the generalized Taylor’s power series is obtained. Some applicat...

In this paper, some theorems of the classical power series are generalized for the fractional power series. Some of these theorems are constructed by using Caputo fractional derivatives. Under some constraints, we proved that the Caputo fractional derivative can be expressed in terms of the ordinary derivative. A new construction of the generalized Taylor’s power series is obtained. Some applic...