Abstract
This paper aims to investigate a class of fractional multi-point boundary value problems at resonance on an infinite interval. New existence results are obtained for the given problem using Mawhin’s coincidence degree theory. Moreover, two examples are given to illustrate the main results.
Highlights
Fractional calculus is a generalization of classical integer-order calculus and has been studied for more than 300 years
From this point of view, fractional differential equations provide a powerful tool for mathematical modeling of complex phenomena in science and engineering practice
An epidemic model of non-fatal disease in a population over a lengthy time interval can be described by fractional differential equations:
Summary
Fractional calculus is a generalization of classical integer-order calculus and has been studied for more than 300 years. Numerous papers discuss BVPs of integer-order differential equations on infinite intervals (see [35,36,37,38]). Motivated by the aforementioned work, this paper uses coincidence degree theory to investigate the existence of solutions for the following fractional BVP:. The main difficulties in solving the present BVP are: Constructing suitable Banach spaces for BVP (1); Since [0, +∞) is noncompact, it is difficult to prove that operator N is L-compact; The theory of Mawhin’s continuation theorem is characterized by higher dimensions of the kernel space on resonance BVPs, constructing projections P and Q is difficult; Estimating a priori bounds of the resonance problem on an infinite interval with dim KerL = 2 (see Section 3, Lemmas 11–16).
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