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Article

Benchohra, Mouffak ; Bouriah, Soufyane ; Lazreg, Jamal E. ; Nieto, Juan J.
Nonlinear Implicit Hadamard’s Fractional Differential Equationswith Delay in Banach Space. (English). Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 55 (2016), issue 1, pp. 15-26
MSC: 26A33, 34A08 | MR 3674595 | Zbl 1362.34010
Keywords:
Hadamard’s fractional derivative; implicit fractional differential equations in Banach space; fractional integral; existence; Gronwall’s lemma for singular kernels; Measure of noncompactness; fixed point
Summary:
In this paper, we establish sufficient conditions for the existence of solutions for nonlinear Hadamard-type implicit fractional differential equations with finite delay. The proof of the main results is based on the measure of noncompactness and the Darbo’s and Mönch’s fixed point theorems. An example is included to show the applicability of our results.
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