Existence and Ulam–Hyers Stability of a Fractional-Order Coupled System in the Frame of Generalized Hilfer Derivatives

Abstract

In this research paper, we consider a class of a coupled system of fractional integrodifferential equations in the frame of Hilfer fractional derivatives with respect to another function. The existence and uniqueness results are obtained in weighted spaces by applying Schauder’s and Banach’s fixed point theorems. The results reported here are more general than those found in the literature, and some special cases are presented. Furthermore, we discuss the Ulam–Hyers stability of the solution to the proposed system. Some examples are also constructed to illustrate and validate the main results.

Dynamical Behavior of a Fractional Order Model for Within-Host SARS-CoV-2

“…Moreover, in the present study, we only discussed the local and global stability of the considered model. While analysis of a fractional-order system, the Ulam-Hyers stability (which guarantees a close exact solution to the system) is also an essential topic [37][38][39], and it will be considered in our future work.…”

On the Generalized Liouville–Caputo Type Fractional Differential Equations Supplemented with Katugampola Integral Boundary Conditions

“…Proof. When ρ I ξ 0 + , ρ I ζ 0 + are applied to the FDEs in (19) and Lemma 2 is used, the solution of the FDEs in (19) for τ ∈ E is…”

“…Substituting the values of a 1 , a 2 , b 1 , b 2 in (22) and ( 23) respectively, we get the solution for the BVP (19).…”

“…The use of fractional differential systems in mathematical representations of physical and engineering processes has drawn considerable interest. See [16][17][18][19][20][21][22] for additional details on the theoretical evolution of such systems. The following is the remainder of the article: Section 2 introduces some fundamental definitions, lemmas, and theorems that support our main results.…”