Approximating solutions of nonlinear hybrid Caputo fractional integro-differential equations via Dhage iteration principle. (English) Zbl 1463.45028

Ardjouni, Abdelouaheb; Djoudi, Ahcene

Ural Math. J. 5, No. 1, 3-12 (2019).

Summary: In this article, we prove the existence and approximation of solutions of the initial value problems of nonlinear hybrid Caputo fractional integro-differential equations. The main tool employed here is the Dhage iteration principle in a partially ordered normed linear space. An example is also given to illustrate the main results.

MSC:

45J05	Integro-ordinary differential equations
34A08	Fractional ordinary differential equations
45L05	Theoretical approximation of solutions to integral equations

Keywords:

approximating solutions; initial value problems; Dhage iteration principle; hybrid fixed point theorem

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