Monotone Iterative Technique for a New Class of Nonlinear Sequential Fractional Differential Equations with Nonlinear Boundary Conditions under the ψ -Caputo Operator

Zidane Baitiche, Choukri Derbazi, Mouffak Benchohra and Juan J. Nieto
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Zidane Baitiche: Laboratoire Equations Différentielles, Department of Mathematics, Faculty of Exact Sciences, Frères Mentouri University Constantine 1, Ain El Bey Way, P.O. Box 325, Constantine 25017, Algeria
Choukri Derbazi: Laboratoire Equations Différentielles, Department of Mathematics, Faculty of Exact Sciences, Frères Mentouri University Constantine 1, Ain El Bey Way, P.O. Box 325, Constantine 25017, Algeria
Mouffak Benchohra: Laboratory of Mathematics, Djillali Liabes University, Sidi-Bel-Abbes 22000, Algeria
Juan J. Nieto: CITMAga, Instituto de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain

Mathematics, 2022, vol. 10, issue 7, 1-11

Abstract: The main crux of this work is to study the existence of extremal solutions for a new class of nonlinear sequential fractional differential equations (NSFDEs) with nonlinear boundary conditions (NBCs) under the ψ -Caputo operator. The obtained outcomes of the proposed problem are derived by means of the monotone iterative technique (MIT) associated with the method of upper and lower solutions. Lastly, the desired findings are well illustrated by an example.

Keywords: sequential ? -Caputo derivative; nonlinear boundary conditions; extremal solutions; monotone iterative technique; upper and lower solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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