Initial Value Problem For Nonlinear Fractional Differential Equations With ψ-Caputo Derivative Via Monotone Iterative Technique
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| Title: | Initial Value Problem For Nonlinear Fractional Differential Equations With ψ-Caputo Derivative Via Monotone Iterative Technique |
| Author: | Derbazi, Choukri Baitiche, Zidane Benchohra, Mouffak Cabada Fernández, Alberto |
| Affiliation: | Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización |
| Subject: | ψ-Caputo fractional derivative | Cauchy problem extremal solutions | Monotone iterative technique | Upper and lower solutions | |
| Date of Issue: | 2020 |
| Publisher: | MDPI |
| Citation: | Derbazi, C.; Baitiche, Z.; Benchohra, M.; Cabada, A. Initial Value Problem For Nonlinear Fractional Differential Equations With ψ-Caputo Derivative Via Monotone Iterative Technique. Axioms 2020, 9, 57 |
| Abstract: | In this article, we discuss the existence and uniqueness of extremal solutions for nonlinear initial value problems of fractional differential equations involving the ψ -Caputo derivative. Moreover, some uniqueness results are obtained. Our results rely on the standard tools of functional analysis. More precisely we apply the monotone iterative technique combined with the method of upper and lower solutions to establish sufficient conditions for existence as well as the uniqueness of extremal solutions to the initial value problem. An illustrative example is presented to point out the applicability of our main results |
| Publisher version: | https://doi.org/10.3390/axioms9020057 |
| URI: | http://hdl.handle.net/10347/23666 |
| DOI: | 10.3390/axioms9020057 |
| E-ISSN: | 2075-1680 |
| Rights: | © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/) Atribución 4.0 Internacional |
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Except where otherwise noted, this item's license is described as © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)