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

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....

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Bibliographic Details
Published inAxioms Vol. 9; no. 2; p. 57
Main Authors Derbazi, Choukri, Baitiche, Zidane, Benchohra, Mouffak, Cabada, Alberto
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.06.2020
Subjects
Boundary value problems
Cauchy problem extremal solutions
Cauchy problems
Differential equations
Functional analysis
Integral equations
Mathematical analysis
monotone iterative technique
Nonlinear equations
Uniqueness
upper and lower solutions
ψ-Caputo fractional derivative
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Summary: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.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms9020057