Existence results by Mönch's fixed point theorem for a tripled system of sequential fractional differential equations

Abstract

<abstract><p>In this paper, we study the existence of the solutions for a tripled system of Caputo sequential fractional differential equations. The main results are established with the aid of Mönch's fixed point theorem. The stability of the tripled system is also investigated via the Ulam-Hyer technique. In addition, an applied example with graphs of the behaviour of the system solutions with different fractional orders are provided to support the theoretical results obtained in this study.</p></abstract>

Stability of a Solution for a Hybrid Fractional Differential Equation

“…In addition to the great importance of studying the existence of solutions to fractional differential equations using the many theories of the fixed point, several studies have been conducted over the years to investigate how stability concepts such as the Mittag-Leffler function, exponential, and Lyapunov stability apply to various types of dynamic systems. Ulam and Hyers, on the other hand, identified previously unknown types of stability known as Ulam-stability [1]. This example is not exclusive, many similar works can be found in [3,5,11,17,31].…”