Abstract
In this paper, we study the periodic boundary value problems for the coupled systems of fractional implicit differential equations. Basing on the coincidence degree theory, we establish the existence and uniqueness theorems. Further, we provide several examples to show our main results.
Highlights
In the past two decades, there has been tremendous interest in studying fractional differential equations (FDEs for short) due to their extensive applications in various fields of engineering and scientific disciplines
5 Conclusion In the present paper, we investigate the existence and uniqueness of solutions for the coupled systems of nonlinear implicit fractional periodic boundary value problems in the frame of Riemann–Liouville fractional derivative
We extend the results of [29, 30] to coupled systems; second, in [29, 30], the authors only studied the existence results based on Lemma 2.1 and established existence theorems under condition (A2)
Summary
In the past two decades, there has been tremendous interest in studying fractional differential equations (FDEs for short) due to their extensive applications in various fields of engineering and scientific disciplines (see [1,2,3,4,5,6,7,8]). Inspired by the above work, in this paper we are mainly concerned with the existence and uniqueness of solutions for the following coupled system of nonlinear implicit FDEs with PBCs:. We remark that our paper investigates the FBVP in the frame of Riemann–Liouville fractional derivative which is more complicated than such a problem involving Caputo fractional derivative, and if α = β = 1, BVP (1.1) can be reduced to the implicit first order differential systems with PBCs. The rest of this paper is built up as follows. Theorem 2.2 Let L : dom L ⊂ X → Y be a Fredholm operator of index zero, Ω ⊂ X be an open bounded set symmetric with 0 ∈ Ω and N : Ω → Y is L-compact.
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