Analytical and numerical analysis for a nonlinear fractional differential equations involving the new Caputo-Fabrizio integral
Samir Lemita1, Nabila Chihi2, Sabrine Lemouchi3
1Echahid Cheikh Larbi Tebessi University, Tebessa, Algeria
2Higher Normal School of Technological Education of Skikda, Skikda, Algeria
3Ecole Normale Supérieure de Ouargla, Ouargla, Algeria
Keywords: fractional differential equation, Caputo-Fabrizio derivative, integro-differential Volterra equation, Schauder fixed point theorem, Nyström method
Abstract
In this paper we consider nonlinear fractional differential equations involving the new Caputo-Fabrizio derivative of order γ ∈]1, 2[. We convert the fractional problem to an equivalent nonlinear Volterra integro-differential equation of the second kind, then we investigate the existence and uniqueness of its solution under certain given conditions by using the Schauder fixed point theorem. Finally, we numerically solve the proposed fractional problem by applying the Nyström method, and we provide some suitable examples to support our study.
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