Solvability of coupled systems of hybrid fractional differential equations and inclusions

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

“…An application of Lemma 4 in [7], Lemma 4 in [9], and eorem 3.1 in [6], we derive an equivalent fractional integral equation to (9). In order to make this paper readable, we present the proof.Let (􏽢 x, 􏽢 y) ∈ E be a solution of (42), (x, y) ∈ E be a solution of problem (1) satisfying Lemma 4.…”

“…Let 0 < α, β < 1, ψ 1 , ψ 2 ∈ AC([0, T], R) and assume that (H1) holds. en, the solution of problem (9) if and only if it is a solution of the following system:…”

“…On the other hand, thanks to the fact that a large number of practical and real world phenomena in the elds of biology, physics, chemistry, and computer network, can be modeled by coupled systems of di erent types of fractional di erential equations. Here, we sketch some references, but not a list of all references is included, such as Hadamard type [8], Caputo [9] and Riemann-Liouville types [10], and Ψ-Hilfer type [11].…”

“…(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. However, it is well known that stability is one of the important dynamic behaviors for fractional-order hybrid differential equations.…”