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

Authors : Zouaoui BEKRI, Vedat Suat ERTÜRK, Pushpendra KUMAR, Venkatesan GOVİNDARAJ

Pages : 299-311

Doi:10.53006/rna.1114063

View : 10 | Download : 5

Publication Date : 2022-09-30

Article Type : Research Paper

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