Existence and H-U stability of a tripled system of sequential fractional differential equations with multipoint boundary conditions

Abstract

In this paper, we introduce a new coupled system of sequential fractional differential equations with coupled boundary conditions. We establish existence and uniqueness results using the Leray–Schauder alternative and Banach contraction principle. We examine the stability of the solutions involved in the Hyers–Ulam type. As an application, we present a few examples to illustrate the main results.

Existence Results for the System of Fractional-Order Sequential Integrodifferential Equations via Liouville–Caputo Sense

“…. , 4 are given by (24). By replacing the constants c2, d2, c3, and d3 in system (15), we can solve problems ( 4) and (5).…”

“…Te methods utilized to attain this outcome were derived from fxed-point theory. Te authors in [24] examined the stability and existence of a tripled system of sequential FDEs with multipoint boundary conditions, whereas the authors in [25] established the existence of solutions for three nonlinear sequential FDEs with nonlocal boundary conditions. Te cited reference [26] contained the conclusions about the existence of solutions for a coupled system of nonlinear diferential equations and inclusions incorporating SFD.…”

Existence of Solutions for Coupled System of Sequential Liouville–Caputo-Type Fractional Integrodifferential Equations

“…The authors employed techniques developed from fixedpoint theory to achieve this result. The work done by the authors of Reference [16] focused on investigating the presence and stability of a tripled system of SFDEs while considering multipoint boundary conditions. The authors of Reference [17] presented a study whereby they established the presence and durability of solutions for three nonlinear SFDEs with nonlocal boundary conditions.…”