Existence and Stability Analysis by Fixed Point Theorems for a Class of Non-Linear Caputo Fractional Differential Equations

Abstract

The main purpose of this work is to establish existence result and stability criteria for a class of fractional order differential equations using fixed point theorems. Existence results are based on Schauder's fixed point theorem, Banach contraction principle and, emphasis is put on the application of the Krasnoselskii's fixed point theorem to establish stability criteria of a specific class of fractional order differential equations. An example is given to show the usefulness of the stability result.

Exponential Stability of Fractional Large-Scale Neutral Stochastic Delay Systems with Fractional Brownian Motion

“…Definition 5. Seemab and Rehman (2018): The solution x l (t) = ϕ(t) of ( 1) is called stable, if for every > 0 and…”

On Nonlinear Fractional Relaxation Differential Equations

“…Recently, many authors have studied various properties of fractional differential equations (see [5,10,11,13,14,19,[21][22][23] and the references therein).…”

Existence, Uniqueness and Stability Solutions of Volterra Integrodifferential Equations With Retarded Argument and Symmetric Matrices

“…(Stochastic, whose basic numerical are addressed in [3,4,5,19,20,21,22, ]). Among the application areas are the biosciences, economics, materials science, medicine, public health, and robotics, in a number of these there is an underlying problem in control theory [23,24,25,26,27,28]. In this paper, we intend to study the existence, uniqueness and stability solution for the following Volterra integro-differential equations with retarded argument and symmetric matrices: The vector functions 𝑛(𝑡, 𝑥, 𝑦, 𝑧, 𝑤, 𝑣) and 𝑚(𝑡, 𝑥, 𝑦, 𝑧, 𝑤, 𝑢) is defined and continuous on the domains:…”