Coupled Fixed Point Results in Banach Spaces with Applications

Mian Bahadur Zada,Thabet Abdeljawad,Muhammad Sarwar,Aiman Mukheimer

doi:10.3390/math9182283

Mian Bahadur Zada, Thabet Abdeljawad + Show 2 more

Open Access

https://doi.org/10.3390/math9182283

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Abstract

The aim of this work is to discuss the existence of solutions to the system of fractional variable order hybrid differential equations. For this reason, we establish coupled fixed point results in Banach spaces.

Highlights

Integral and fractional differential operators have been popular in mathematical models
The earthquake’s non-linear oscillation can be framed with fractional derivatives [1], and fractional derivatives combined with the fluid dynamic traffic design can eliminate the shortfall originating from the assumption of continuum traffic flow [2]
The integrals and derivatives whose order is a function of specific variables catch the attention because of their applied significance in different fields of research, such as: multifractional Gaussian noises [9], mechanical applications [10], FIR filters [11], anomalous diffusion modeling [12]

Summary

Introduction

Integral and fractional differential operators have been popular in mathematical models It is the last one hundred years in which the majority of the fractional problems in scientific application and engineering have been discovered. To check the existence of solution, we use fixed point theory, because the problem of the existence of solution usually turns into the problem of finding a fixed point of a particular mapping Due to this fact, the results of fixed point theory could be implemented to the get results of an operator equation. A useful result for the existence of solution to Equation p2q is the Krasnosel’skii [16] fixed point theorem. Motivated by the work of [15], we will discuss the existence of solution to the following system of fractional variable order hybrid differential equations:. For the existence of solution to the system p3q, we establish coupled fixed point results in Banach spaces by utilizing the results of Amar et al [17]

Preliminaries

Coupled Fixed Point Theorems

Applications