On impulsive nonlocal integro-initial value problems involving multi-order Caputo-type generalized fractional derivatives and generalized fractional integrals
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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
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Bibliographic 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
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https://doi.org/10.1186/s13662-019-2183-4Sponsors
This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia under grant no. (RG-1-130-39)
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© 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