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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Zidane Baitiche & Choukri Derbazi & Mouffak Benchohra & Juan J. Nieto, 2022. "Monotone Iterative Technique for a New Class of Nonlinear Sequential Fractional Differential Equations with Nonlinear Boundary Conditions under the ψ -Caputo Operator," Mathematics, MDPI, vol. 10(7), pages 1-11, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1173-:d:786719
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