Initial Value Problem For Nonlinear Fractional Differential Equations With ψ-Caputo Derivative Via Monotone Iterative Technique

Derbazi, ChoukriBaitiche, ZidaneBenchohra, MouffakCabada Fernández, Alberto2020-11-112020-11-112020Derbazi, 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, 57http://hdl.handle.net/10347/23666In 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 resultseng© 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 Internacionalhttp://creativecommons.org/licenses/by/4.0/ψ-Caputo fractional derivativeCauchy problem extremal solutionsMonotone iterative techniqueUpper and lower solutionsInitial Value Problem For Nonlinear Fractional Differential Equations With ψ-Caputo Derivative Via Monotone Iterative Techniquejournal article10.3390/axioms90200572075-1680open access