Progress in Fractional Differentiation & Applications

Author Country (or Countries)

Saudi Arabia


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.

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