On an integro-differential fractional nonlinear Volterra-Caputo equation
S. Guemar1, H. Guebbai2, S. Lemita3
1UniversitГ© Yahia Fares MГ©dГ©a. PГґle urbain, MГ©dГ©a, AlgГ©rie
2University of Guelma, Guelma, AlgГ©rie
3'Ecole Normale SupГ©rieure de Ouargla, CitГ© Ennacer, Ouargla, AlgГ©rie
Keywords: Volterra equation, integro-differential-fractional equation, fixed point, nonlinear equation, product integration method
Abstract
In this paper, we study a nonlinear integro-differential Volterra equation with a fractional Caputo derivative. Based on techniques derived from a study of classical Volterra equations, namely Picard's iterative sequence and the product integration method, we propose a complete analytical and numerical study of this equation. Our study is closed by the development of two numerical examples.
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