Existence Results for Hybrid Stochastic Differential Equations Involving $\psi$-Hilfer Fractional Derivative

Abstract

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

Existence and Stability for a Coupled Hybrid System of Fractional Differential Equations with Atangana–Baleanu–Caputo Derivative

“…For instance, Baleanu [2] applied Caputo fractional-order hybrid di erential equations to analyze a thermostat model. Other contributions on fractional-order hybrid di erential equations involving the Hadamard derivative [3], Riemann derivative [4], Hilfer derivative [5], and Atangana derivative [6,7] (ABC).…”

“…(1) e above-given results [2][3][4][5][6][7] consider single fractional-order hybrid differential equations, while we consider coupled fractional-order hybrid systems. (2) e work in [8][9][10][11] investigated the existence of solutions or initial value boundary value problem.…”