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Existence and Stability of Nonlinear Implicit Caputo-Exponential Fractional Differential Equations |
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PP: 91-105 |
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doi:10.18576/pfda/080106
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Author(s) |
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Mouffak Benchohra,
Jamal Eddine Lazreg,
Bessem Samet,
Yong Zhou,
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Abstract |
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| 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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