Some novel analysis of two different Caputo-type fractional-order boundary value problems

Year 2022, Volume: 5 Issue: 3, 299 - 311, 30.09.2022

Zouaoui Bekrı , Vedat Suat Ertürk , Pushpendra Kumar , Venkatesan Govindaraj

https://doi.org/10.53006/rna.1114063

Cited By: 5

Abstract

Nowadays, a number of classical order results are being analyzed in
the sense of fractional derivatives. In this research work, we
discuss two different boundary value problems. In the first half of
the paper, we generalize an integer-order boundary value problem
into fractional-order and then we demonstrate the existence and
uniqueness of the solution subject to the Caputo fractional
derivative. First, we recall some results and then justify our main
results with the proofs of the given theorems. We conclude our
results by presenting an illustrative example. In the other half of
the paper, we extend the Banach's contraction theorem to prove the
existence and uniqueness of the solution to a sequential Caputo
fractional-order boundary value problem.

Keywords

Caputo fractional derivative, Existence and uniqueness, Boundary value problem

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