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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

Special Issues: Initial and Boundary Value Problems for Differential Equations

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 Fréchet spaces associated with the concept of measures of noncompactness. An application of the main result has been included.
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Keywords 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. AIMS Mathematics, 2020, 5(1): 15-25. doi: 10.3934/math.2020002

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