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On a Periodic Boundary Value Problem for Fractional Quasilinear Differential Equations with a Self-Adjoint Positive Operator in Hilbert Spaces

Author

Listed:
  • Mikhail Kamenskii

    (Faculty of Mathematics, Voronezh State University, 394018 Voronezh, Russia)

  • Garik Petrosyan

    (Faculty of Physics and Mathematics, Voronezh State Pedagogical University, 394043 Voronezh, Russia)

  • Paul Raynaud de Fitte

    (Raphael Salem Mathematics Laboratory, University of Rouen Normandy, 76821 Rouen, France)

  • Jen-Chih Yao

    (Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

Abstract

In this paper we study the existence of a mild solution of a periodic boundary value problem for fractional quasilinear differential equations in a Hilbert spaces. We assume that a linear part in equations is a self-adjoint positive operator with dense domain in Hilbert space and a nonlinear part is a map obeying Carathéodory type conditions. We find the mild solution of this problem in the form of a series in a Hilbert space. In the space of continuous functions, we construct the corresponding resolving operator, and for it, by using Schauder theorem, we prove the existence of a fixed point. At the end of the paper, we give an example for a boundary value problem for a diffusion type equation.

Suggested Citation

  • Mikhail Kamenskii & Garik Petrosyan & Paul Raynaud de Fitte & Jen-Chih Yao, 2022. "On a Periodic Boundary Value Problem for Fractional Quasilinear Differential Equations with a Self-Adjoint Positive Operator in Hilbert Spaces," Mathematics, MDPI, vol. 10(2), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:219-:d:722614
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