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On Solvability of Fractional ( p , q )-Difference Equations with ( p , q )-Difference Anti-Periodic Boundary Conditions

Author

Listed:
  • Ravi P. Agarwal

    (Department of Mathematics, Texas A& M University, Kingsville, TX 78363-8202, USA)

  • Hana Al-Hutami

    (Nonlinear Analysis and Applied Mathematics (NAAM)—Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Bashir Ahmad

    (Nonlinear Analysis and Applied Mathematics (NAAM)—Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

Abstract

We discuss the solvability of a ( p , q ) -difference equation of fractional order α ∈ ( 1 , 2 ] , equipped with anti-periodic boundary conditions involving the first-order ( p , q ) -difference operator. The desired results are accomplished with the aid of standard fixed point theorems. Examples are presented for illustrating the obtained results.

Suggested Citation

  • Ravi P. Agarwal & Hana Al-Hutami & Bashir Ahmad, 2022. "On Solvability of Fractional ( p , q )-Difference Equations with ( p , q )-Difference Anti-Periodic Boundary Conditions," Mathematics, MDPI, vol. 10(23), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4419-:d:982214
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    References listed on IDEAS

    as
    1. Cai, Qing-Bo & Zhou, Guorong, 2016. "On (p, q)-analogue of Kantorovich type Bernstein–Stancu–Schurer operators," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 12-20.
    2. Chanon Promsakon & Nattapong Kamsrisuk & Sotiris K. Ntouyas & Jessada Tariboon, 2018. "On the Second-Order Quantum - Difference Equations with Separated Boundary Conditions," Advances in Mathematical Physics, Hindawi, vol. 2018, pages 1-9, December.
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