Measure of noncompactness and fractional integro-differential equations with state-dependent nonlocal conditions in Fréchet spaces

Mouffak Benchohra; Zohra Bouteffal; Johnny Henderson; Sara Litimein; Mouffak Benchohra; Zohra Bouteffal; Johnny Henderson; Sara Litimein

doi:10.3934/math.2020002

AIMS Mathematics

2020, Volume 5, Issue 1: 15-25. doi: 10.3934/math.2020002

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Measure of noncompactness and fractional integro-differential equations with state-dependent nonlocal conditions in Fréchet spaces

1.
Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P. O. Box 89, 22000, Sidi Bel-Abbes, Algeria
2.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
3.
Department of Mathematics, Faculty of Exact Sciences, Mustapha Stambouli University of Mascara, P. O. Box 305, 29000, Algeria
4.
Department of Mathematics, Baylor University, Waco, Texas 76798-7328, USA

Received: 06 March 2019 Accepted: 09 October 2019 Published: 15 October 2019
MSC : 34G20

This paper deals with the existence of mild solutions for non-linear fractional integrodifferential equations with state-dependent nonlocal conditions. The technique used is a generalization of the classical Darbo fixed point theorem for Frechet spaces associated with the concept of measures ′ of noncompactness. An application of the main result has been included.
- fractional integro-differential equations,
- solution operator,
- mild solution,
- fixed point,
- state-dependent nonlocal condition,
- measure of noncompactness,
- Fréchet space
Citation: Mouffak Benchohra, Zohra Bouteffal, Johnny Henderson, Sara Litimein. Measure of noncompactness and fractional integro-differential equations with state-dependent nonlocal conditions in Fréchet spaces[J]. AIMS Mathematics, 2020, 5(1): 15-25. doi: 10.3934/math.2020002

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Abstract

This paper deals with the existence of mild solutions for non-linear fractional integrodifferential equations with state-dependent nonlocal conditions. The technique used is a generalization of the classical Darbo fixed point theorem for Frechet spaces associated with the concept of measures ′ of noncompactness. An application of the main result has been included.

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