Vol. 22(2021) No. 2



  Notes on Krasnoselskii-type fixed-point theorems and their application to fractional hybrid differential problems
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Fixed Point Theory, Volume 22, No. 2, 2021, 465-480, July 1st, 2021

DOI: 10.24193/fpt-ro.2021.2.31

Authors: H. Akhadkulov, T.Y. Ying, A.B. Saaban, M.S. Noorani and H. Ibrahim

Abstract: In this paper we prove a new version of Kransoselskii's fixed-point theorem under a (ψ, θ, ϕ)-weak contraction condition. The theoretical result is applied to prove the existence of a solution of the following fractional hybrid differential equation involving the Riemann-Liouville differential and integral operators orders of 0<α<1 and β>0:

where Dα is the Riemann-Liouville fractional derivative order of α, Iβ is Riemann-Liouville fractional integral operator order of β>0, J=[t0, t0+a], for some fixed t0∈ ℝ, a>0 and the functions f : J × ℝ → ℝ and g : J × ℝ × ℝ → ℝ satisfy certain conditions. An example is also furnished to illustrate the hypotheses and the abstract result of this paper.

Key Words and Phrases: Fixed-point theorem, Riemann-Liouville fractional derivative, hybrid initial value problem.

2010 Mathematics Subject Classification: 26A33, 34A08, 34A12, 47H07, 47H10.

Published on-line: July 1st, 2021.

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