We study a coupled system of implicit differential equations with fractional-order boundary conditions and the Riemann–Liouville derivative. The existence, uniqueness, at least one solution are established by applying Banach contraction Leray–Schauder fixed point theorem. Furthermore, Hyers–Ulam type stabilities discussed. An example is presented to illustrate our main result. suggested general...

in the present paper, measure differential equations involving the distributional henstock-kurzweil integral are investigated. theorems on the existence and structure of the set of solutions are established by using schauder$^prime s$ fixed point theorem and vidossich theorem. two examples of the main results paper are presented. the new results are generalizations of some previous results in t...

In this manuscript, we examine both the existence and stability of solutions boundary value problems Hadamard-type fractional differential equations variable order. New outcomes are obtained in paper based on Darbo’s fixed point theorem (DFPT) combined with Kuratowski measure noncompactness (KMNC). We construct an example to illustrate validity observed results.

The paper is devoted to studying the solutions of boundary value problem for nonlinear fractional differential equation with Riemann-Liouville type history-state-based variable-order derivative. Using Schauder fixed point theorem and Banach thoerem, we prove existence uniqueness in Hölder space. Lastly, two examples are given show applicability theorems.

This paper is devoted to investigating one type of nonlinear two-term fractional order delayed differential equations involving Caputo derivatives. The Leray–Schauder alternative fixed-point theorem and Banach contraction principle are applied analyze the existence uniqueness solutions problem with infinite delay. Additionally, Hyers–Ulam stability considered for delay conditions.

*Correspondence: [email protected] 3Department of Mathematics, University of Hong Kong, Pokfulam, Hong Kong Full list of author information is available at the end of the article Abstract This paper focuses on a certain type of periodic boundary value problems for first-order impulsive difference equations with time delay. Notions of lower and upper solutions are introduced, with which two new co...