Nonlinear implicit Hadamard’s fractional differential equations with delay in Banach space. (English) Zbl 1362.34010

Benchohra, Mouffak; Bouriah, Soufyane; Lazreg, Jamal E.; Nieto, Juan J.

Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 55, No. 1, 15-26 (2016).

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.

MSC:

34A08

Fractional ordinary differential equations

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

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