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Applications of Structural Nabla Derivatives on Time Scales to Dynamic Equations

Author

Listed:
  • Amin Benaissa Cherif

    (Department of Mathematics, Faculty of Mathematics and Informatics, University of Science and Technology of Oran Mohamed-Boudiaf (USTOMB), El Mnaouar, BP 1505, Bir El Djir, Oran 31000, Algeria)

  • Bouharket Bendouma

    (Ibn Khaldoun, Tiaret University, Zaâroura, P.O. Box 78, Tiaret 14000, Algeria)

  • Khaled Zennir

    (Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
    Department of Mathematics, University 20 Août 1955, Skikda 21000, Algeria)

  • Svetlin G. Georgiev

    (Department of Mathematics, Sorbonne University, 75005 Paris, France)

  • Keltoum Bouhali

    (Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia)

  • Taha Radwan

    (Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia
    Department of Mathematics and Statistics, Faculty of Management Technology and Information Systems, Port Said University, Port Said 42511, Egypt)

Abstract

We present here more general concepts of Hausdorff derivatives (structural Nabla derivatives) on a timescale. We examine structural Nabla integration on temporal scales. Using the fixed-point theorem, we establish adequate criteria for the question of existence and uniqueness of the solution to an initial value problem characterized by structural Nabla derivatives on timescales. Furthermore, some features of the new operator are proven and illustrated by using concrete examples.

Suggested Citation

  • Amin Benaissa Cherif & Bouharket Bendouma & Khaled Zennir & Svetlin G. Georgiev & Keltoum Bouhali & Taha Radwan, 2024. "Applications of Structural Nabla Derivatives on Time Scales to Dynamic Equations," Mathematics, MDPI, vol. 12(11), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1688-:d:1404553
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