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Existence and uniqueness results for nonlinear hybrid implicit Caputo-Hadamard fractional differential equations

Abdelouaheb Ardjouni, Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, Souk Ahras, 41000, Algeria, Adel Lachouri, Ahcene Djoudi, Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, Souk Ahras, 41000, Algeria, Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, Souk Ahras, 41000, Algeria.
2019 Open Journal of Mathematical Analysis  

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In this paper, we use the Banach fixed point theorem to obtain the existence, interval of existence and uniqueness of solutions for nonlinear hybrid implicit Caputo-Hadamard fractional differential equations. We also use the generalization of Gronwall's inequality to show the estimate of the solutions.
doi:10.30538/psrp-oma2019.0044 fatcat:2ou2a5rgi5b3xemmzf2katwxuu
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Abdelouaheb Ardjouni, Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, Souk Ahras, 41000, Algeria, Adel Lachouri, Ahcene Djoudi, Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, Souk Ahras, 41000, Algeria, Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, Souk Ahras, 41000, Algeria.. "Existence and uniqueness results for nonlinear hybrid implicit Caputo-Hadamard fractional differential equations." Open Journal of Mathematical Analysis 3.2 (2019) 106-111