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Progress in Fractional Differentiation & Applications

Author Country (or Countries)

Saudi Arabia

Abstract

In this paper, the existence and stability of solutions for the following fractional problem with Caputo--Exponential fractional derivative are discussed eζ eζ c D0+ ψ (α ) = θ (α , ψ (α ), c D0+ ψ (α )), for each, α ∈ Θ := [0, b], b > 0, 0 < ζ ≤ 1, ψ(0) = ψ0. We use Schauder’s fixed point theorem, the nonlinear alternative of Leray–Schauder type and Banach contraction principle to demonstrate our results. Two examples are provided to demonstrate the relevance of our results.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/080106

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