Existence and Ulam stability for nonlinear implicit differential equations with Riemann-Liouville fractional derivative

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URI: http://hdl.handle.net/10347/21019
ISSN: 0420-1213
E-ISSN: 2391-4661
DOI: 10.1515/dema-2019-0032

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2019

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De Gruyter
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In this paper, we establish the existence and uniqueness of solutions for a class of initial value problem for nonlinear implicit fractional differential equations with Riemann-Liouville fractional derivative, also, the stability of this class of problem. The arguments are based upon the Banach contraction principle and Schaefer’s fixed point theorem. An example is included to show the applicability of our results

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Riemann-Liouville fractional derivative| Initial value problem| Existence| Uniqueness| Ulam stability| Fixed point theorem

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Benchohra, M., Bouriah, S., & Nieto, J. J. (2019). Existence and Ulam stability for nonlinear implicit differential equations with Riemann-Liouville fractional derivative, Demonstratio Mathematica, 52(1), 437-450. doi: https://doi.org/10.1515/dema-2019-0032

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The research of J.J. Nieto has been partially supported by the AEI of Spain under Grant MTM2016-75140-P and co-financed by European Community fund FEDER

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© 2019 Mouffak Benchohra et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution alone 4.0 License

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Estatística, Análise Matemática e Optimización