Existence of solutions for hybrid modified ABC-fractional differential equations with p-Laplacian operator and an application to a waterborne disease model

In this article, we investigate some necessary and sufficient conditions required for the existence of solutions for modified ABC-fractional differential equations (mAB-FDEs) with pLaplacian operator. We also study the uniqueness and Hyers-Ulam stability (HU-stability) for the solutions of the presumed mABC-FDEs system. For the recently developed mABC-operator, such a problem has not yet studied also our problem is more general than those in the available literature. (c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Automated summary

In this article, necessary and sufficient conditions for the existence of solutions of modified ABC-fractional differential equations (mAB-FDEs) with pLaplacian operator are investigated. The uniqueness and Hyers-Ulam stability (HU-stability) of the presumed mABC-FDEs system are also studied. This problem has not yet been studied for the recently developed mABC-operator and our problem is more general than those in the available literature.