Nonlinear boundary value problem for implicit differential equations of fractional order in Banach spaces


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	Nonlinear boundary value problem for implicit differential equations of fractional order in Banach spaces


	Fixed Point Theory, Volume 18, No. 2, 2017, 457-470, June 1st, 2017 DOI: 10.24193/fpt-ro.2017.2.36 Authors: M. Benchohra, S. Bouriah and M.A. Darwish Abstract: In this paper, we establish sufficient conditions for the existence of solutions for a class of boundary value problem for implicit fractional differential equations with Caputo fractional derivative. We apply the technique of measure of noncompactness and the fixed point theorems of Darbo and Mönch. As an application, two examples are included to show the applicability of our results. Key Words and Phrases: Boundary value problem, Caputo's fractional derivative, implicit fractional differential equations in Banach space, fractional integral, existence, Gronwall's lemma for singular kernels, measure of noncompactness, fixed point. 2010 Mathematics Subject Classification: 26A33, 34A08, 47H10. Published on-line: June 1st, 2017. Abstract pdf Fulltext pdf Back to volume's table of contents