On impulsive nonlocal integro-initial value problems involving multi-order Caputo-type generalized fractional derivatives and generalized fractional integrals
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| Title: | On impulsive nonlocal integro-initial value problems involving multi-order Caputo-type generalized fractional derivatives and generalized fractional integrals |
| Author: | Ahmad, Bashir Alghanmi, Madeaha Nieto Roig, Juan José Alsaedi, Ahmed |
| Affiliation: | Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización |
| Subject: | Multi-order fractional derivatives | Impulse | Caputo-type generalized fractional derivative | Fractional integral | Extremal solutions | |
| Date of Issue: | 2019 |
| Publisher: | Springer |
| Citation: | Ahmad, B., Alghanmi, M., Nieto, J.J. et al. On impulsive nonlocal integro-initial value problems involving multi-order Caputo-type generalized fractional derivatives and generalized fractional integrals. Adv Differ Equ 2019, 247 (2019). https://doi.org/10.1186/s13662-019-2183-4 |
| Abstract: | In this paper, we present sufficient criteria ensuring the existence and uniqueness of solutions for nonlinear impulsive multi-order Caputo-type generalized fractional differential equations supplemented with nonlocal integro-initial value conditions involving generalized fractional integrals. Extremal solutions for the given problem are also discussed. The main tools of our study include Krasnoselskii’s fixed point theorem, Banach contraction mapping principle and monotone iterative technique. Examples are constructed for illustrating the obtained results |
| Publisher version: | https://doi.org/10.1186/s13662-019-2183-4 |
| URI: | http://hdl.handle.net/10347/21167 |
| DOI: | 10.1186/s13662-019-2183-4 |
| E-ISSN: | 1687-1847 |
| Rights: | © The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/),which permits unrestricted use, distribution, and reproduction in anymedium, providedyou give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made |
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Except where otherwise noted, this item's license is described as © The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/),which permits unrestricted use, distribution, and reproduction in anymedium, providedyou give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made