Analytical and numerical study of a nonlinear Volterra integro-differential equation with the Caputo-Fabrizio fractional derivative. (English) Zbl 1535.45003
In the context of fractional calculus and fractional integro-differential equations, several notions and applications have been considered and studied by various researchers.
In the present paper, the authors study a nonlinear integro-differential equation of Volterra type with a Caputo fractional derivative without singular kernel. In Section 2, a left-sided Caputo-Fabrizio fractional derivative is defined and its fundamental properties are discussed. Employing some specific Lipschitz conditions an existence and uniqueness theorem for solutions of the considered Volterra integro-differential equation is stated and proved. Finally, a numerical unique solution is constructed and its consistency with the analytic solution is discussed. MATLAB and C++ programming are used to solve three concrete examples.
In the present paper, the authors study a nonlinear integro-differential equation of Volterra type with a Caputo fractional derivative without singular kernel. In Section 2, a left-sided Caputo-Fabrizio fractional derivative is defined and its fundamental properties are discussed. Employing some specific Lipschitz conditions an existence and uniqueness theorem for solutions of the considered Volterra integro-differential equation is stated and proved. Finally, a numerical unique solution is constructed and its consistency with the analytic solution is discussed. MATLAB and C++ programming are used to solve three concrete examples.
Reviewer: Deshna Loonker (Jodhpur)
MSC:
| 45J05 | Integro-ordinary differential equations |
| 45D05 | Volterra integral equations |
| 26A33 | Fractional derivatives and integrals |
| 65R20 | Numerical methods for integral equations |
Keywords:
nonlinear integro-differential equation; Caputo-Fabrizio fractional derivative; convergence; existence and uniqueness of solution; nonsingular kernelReferences:
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