Analytical Study of Two Nonlinear Coupled Hybrid Systems Involving Generalized Hilfer Fractional Operators

Abstract

In this research paper, we dedicate our interest to an investigation of the sufficient conditions for the existence of solutions of two new types of a coupled systems of hybrid fractional differential equations involving ϕ-Hilfer fractional derivatives. The existence results are established in the weighted space of functions using Dhage’s hybrid fixed point theorem for three operators in a Banach algebra and Dhage’s helpful generalization of Krasnoselskii fixed- point theorem. Finally, simulated examples are provided to demonstrate the obtained results.

Hybrid System of Proportional Hilfer-Type Fractional Differential Equations and Nonlocal Conditions with Respect to Another Function

“…In [29], the authors studied the existence and Ulam-Hyers stability results of a coupled system of ψ-Hilfer sequential fractional differential equations. In [30], by using Krasnosel'ski ȋ's fixed point theorem, the existence of solutions are established for the following nonlinear system involving generalized Hilfer fractional operators…”

On a (k;chi)-Hilfer fractional system with coupled nonlocal boundary conditions including various fractional derivatives and Riemann–Stieltjes integrals

“…Coupled systems of FDEs with different kinds of boundary conditions is one of the subjects in applied mathematics, which have been the interest of many researchers; see, for instance, [5,10] and references therein. Hilfer coupled systems two-point boundary conditions were studied in [7], involving multipoint nonlocal boundary conditions in [13], involving Riemann-Stieltjes integral multistrip boundary conditions in [27], with nonlocal integral boundary conditions in [11], with nonlocal integro-multistrip-multipoint boundary conditions in [1] and coupled systems of nonlinear ψ-Hilfer hybrid fractional differential equations in [24] and [8]. Luca [23] studied a system of Riemann-Liouville fractional differential equations supplemented with coupled boundary conditions, which involve diverse fractional derivatives and Riemann-Stieltjes integrals.…”

Characteristics of a Subclass of Analytic Functions Introduced by Using a Fractional Integral Operator

“…An investigation of the sufficient conditions for the existence of solutions of two new types of coupled systems of hybrid fractional differential equations involving  -Hilfer fractional derivatives is conducted in [7]. Several algebraic aspects of the fuzzy Caputo fractional derivative and fuzzy Atangana-Baleanu fractional derivative operator in the Caputo sense are investigated in [8].…”