In this paper, we study the existence and uniqueness results of a fractional hybrid boundary value problem with multiple derivatives \(\psi-\)Caputo different orders. Using useful generalization Krasnoselskii’s fixed point theorem, have established at least one solution, while solution is derived by Banach's point. The last section devoted to an example that illustrates applicability our results.

in this paper, a numerical efficient method is proposed for the solution of time fractionalmobile/immobile equation. the fractional derivative of equation is described in the caputosense. the proposed method is based on a finite difference scheme in time and legendrespectral method in space. in this approach the time fractional derivative of mentioned equationis approximated by a scheme of order o...

Fractional differential equations arise in many engineering and scientific disciplines as the mathematical modeling of systems and processes in various fields, such as physics, mechanics, aerodynamics, chemistry, and engineering and biological sciences, involves derivatives of fractional order. Fractional differential equations also provide an excellent tool for the description of memory and he...

Fractional differential equations can model various complex problems in physics and engineering, but there is no universal method to solve fractional models precisely. This paper offers a new hope for this purpose by coupling the homotopy perturbation with Aboodh transform. The hybrid technique leads simple approach finding an approximate solution, which converges fast exact one less computing ...

In this paper, we discuss the existence of solutions for hybrid stochastic differential equations (HSDEs) with $\psi$-Hilfer fractional derivative. The main tool used in our study is associated technique fixed point theorems due to Dhage.

In this paper, we are concerned with seeking exact solutions for fractional differential-difference equations by an extended Riccati sub-ODE method. The fractional derivative is defined in the sense of the modified Riemann-liouville derivative. By a combination of this method and a fractional complex transformation, the iterative relations from indices n to n ± 1 are established. As for applica...

In this article we have applied a numerical finite difference method to solve the Black-Scholes European and American option pricing both presented by fractional differential equations in time and asset.

Chaos synchronization of coupled fractional order differential equation is receiving increasing attention because of its potential applications in secure communications and control processing. The aim of this paper is synchronization between two identical or different delay fractional-order chaotic systems in finite time. At first, the predictor-corrector method is used to obtain the solutions ...