On the Solvability of Iterative Systems of Fractional-Order Differential Equations with Parameterized Integral Boundary Conditions

Abstract

The aim of this paper is to determine the eigenvalue intervals of $\mu_{\mathtt{k}},~1\le \mathtt{k}\le \mathtt{n}$ for which an iterative system of a class of fractional-order differential equations with parameterized integral boundary conditions (BCs) has at least one positive solution by means of standard fixed point theorem of cone type. To the best of our knowledge, this will be the first time that we attempt to reach such findings for the topic at hand in the literature. The obtained results in the paper are illustrated with an example of their feasibility.

Keywords

• boundary value problem
• fixed-point theorems
• fractional derivative
• kernel
• positive solution