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

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.

Solvability and stability of nonlinear hybrid ∆-difference equations of fractional-order

In this paper, we study a type of nonlinear hybrid Δ-difference equations of fractional-order. The main objective is to establish some stability criteria including the Ulam–Hyers stability, generalized Ulam–Hyers stability together with the Mittag-Leffler–Ulam–Hyers stability for the addressed problem. Prior to the stabilization processes, solvability criteria for the existence and uniqueness of solutions are considered. For this purpose, a hybrid fixed point theorem for triple operators and the Banach contraction mapping principle are applied, respectively. For the sake of illustrating the practical impact of the proposed theoretical criteria, we finish the paper with particular examples.

On the Hybrid Fractional Differential Equations with Fractional Proportional Derivatives of a Function with Respect to a Certain Function

This paper deals with a new class of hybrid fractional differential equations with fractional proportional derivatives of a function with respect to a certain continuously differentiable and increasing function ϑ. By means of a hybrid fixed point theorem for a product of two operators, an existence result is proved. Furthermore, the sufficient conditions of the continuous dependence on the given parameters are investigated. Finally, a simulative example is given to highlight the acquired outcomes.

The generalized U–H and U–H stability and existence analysis of a coupled hybrid system of integro-differential IVPs involving φ-Caputo fractional operators

We investigate the existence and uniqueness of solutions to a coupled system of the hybrid fractional integro-differential equations involving φ-Caputo fractional operators. To achieve this goal, we make use of a hybrid fixed point theorem for a sum of three operators due to Dhage and also the uniqueness result is obtained by making use of the Banach contraction principle. Moreover, we explore the Ulam–Hyers stability and its generalized version for the given coupled hybrid system. An example is presented to guarantee the validity of our existence results.

Hybrid Fixed Point Theorem with Applications to Forced Damped Oscillations and Infinite Systems of Fractional Order Differential Equations

In this manuscript, hybrid common fixed point results in the setting of a b -metric space are established. Our results generalized the results of Fisher, Khan, and Piri et al. for set-valued mapping in b -metric spaces. Applications to forced damped oscillations, infinite systems of fractional order differential equations, and system of functional equations are also studied. We construct an example to support our main result.

Existence and Extremal Solution of Boundary Value Problem for Nonlinear Hybrid Fractional Differential Equation in Banach Algebras

In this work we study the existence and extremal solution for the boundary value problem of the nonlinear hybrid fractional differential equation by using hybrid fixed point theorem in Banach Algebra due to Dhage’s theorem.

Existence of Mild solutions of Fractional order Hybrid Deferential Equations with Impulses

This article derive sufficient conditions for existence of mild solution for the hybrid fractional order differential equation with impulses of the form eq1 on a Banach space X over interval [0,T]. The results are obtained using the concept of hybrid fixed point theorem. Finally an illustration is added to show validation of the derived results.

A coupled hybrid fixed point theorem involving the sum of two coupled operators in a partially ordered Banach space with applications

In this paper we prove a coupled hybrid fixed point theorem involving the sum of two coupled operators in a partially ordered Banach space and apply to a pair of nonlinear second order coupled linearly perturbed hybrid differential equations with the periodic boundary conditions for proving the existence and approximation of coupled solutions under certain mixed hybrid conditions. The abstract existence result of the coupled periodic boundary value problems is also illustrated by furnishing a numerical example.

Existence Results of Initial Value Problems for Hybrid Fractional Sum-Difference Equations

We consider a hybrid fractional sum-difference initial value problem and a hybrid fractional sequential sum-difference initial value problem. The existence results of these two problems are proved by using the hybrid fixed point theorem for three operators in a Banach algebra and the generalized Krasnoselskii’s fixed point theorem, respectively.