On a Coupled Impulsive Fractional Integrodifferential System with Hadamard Derivatives

Abstract

The main intention of the present research study is focused on the analysis of coupled impulsive fractional integrodifferential system having Hadamard derivatives. With the help of fixed point theorem attributed to Krasnoselskii's, we investigate desired existence and uniqueness results. Moreover, we present different kinds of stability such as Hyers-Ulam stability, generalized Hyers-Ulam stability, Hyers-Ulam-Rassias stability, and generalized Hyers-Ulam-Rassias stability using the classical technique of functional analysis. Next, an example is designed to examine our findings based on the procedures applied in the theorems.

Approximate solutions of generalized logistic equation

“…The present author previously studied conditional Ulam stability [37,38,41]. However, note that these studies mainly dealt with the conditional Ulam stability of the differential equations y ′ = y(y−1), y ′ = y 2 3 −y and y−xy ′ −(y ′ ) 2 = 0, which are not included in (1) or the Richards model. Conditional Ulam stability for discrete logistic equations has been previously studied.…”

Analysis of q‐fractional coupled implicit systems involving the nonlocal Riemann–Liouville and Erdélyi–Kober q‐fractional integral conditions

“…The coupled system of differential equations is very important to investigate because this type of system appears in many situations of applied nature. The reader may consult for more information and examples [17–21]. The development of differential models for complex systems requires the use of fractional calculus and coupled in particular, making them one of the most powerful tools in modern mathematics.…”

Analysis of implicit system of fractional order via generalized boundary conditions

“…Recently, researchers continuously focus on studying the solution of s in the sense of four main types of stability, that is, Ulam-Hyers stability ( ), generalized Ulam-Hyers stability ( ), Ulam-Hyers-Rassias stability ( ), and generalized Ulam-Hyers-Rassias stability ( ). Ulam's type stability was initially introduced by Ulam [18] in 1940 and has since been investigated and generalized by a number of mathematicians using various approaches [19][20][21][22][23][24].…”

“…Recently, researchers continuously focus on studying the solution of $$$ \mathcal{FDE}s $$$ in the sense of four main types of stability, that is, Ulam–Hyers stability ( $$$ \mathcal{UHS} $$$), generalized Ulam–Hyers stability ( $$$ \mathcal{GUHS} $$$), Ulam–Hyers–Rassias stability ( $$$ \mathcal{UHRS} $$$), and generalized Ulam–Hyers–Rassias stability ( $$$ \mathcal{GUHRS} $$$). Ulam's type stability was initially introduced by Ulam [18] in 1940 and has since been investigated and generalized by a number of mathematicians using various approaches [19–24].…”