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On System of Variable Order Nonlinear p-Laplacian Fractional Differential Equations with Biological Application

Author

Listed:
  • Hasib Khan

    (Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia)

  • Jehad Alzabut

    (Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
    Department of Industrial Engineering, OSTİM Technical University, Ankara 06374, Turkey)

  • Haseena Gulzar

    (Department of Biotechnology, Shaheed Benazir Bhutto University, Sheringal Dir Upper 18000, Pakistan)

  • Osman Tunç

    (Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University Campus, Van 65080, Turkey)

  • Sandra Pinelas

    (Departamento de Ciencias Exatas e Engenharia, Academia Militar, 2720-113 Amadora, Portugal
    Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal)

Abstract

The study of variable order differential equations is important in science and engineering for a better representation and analysis of dynamical problems. In the literature, there are several fractional order operators involving variable orders. In this article, we construct a nonlinear variable order fractional differential system with a p-Laplacian operator. The presumed problem is a general class of the nonlinear equations of variable orders in the ABC sense of derivatives in combination with Caputo’s fractional derivative. We investigate the existence of solutions and the Hyers–Ulam stability of the considered equation. The presumed problem is a hybrid in nature and has a lot of applications. We have given its particular example as a waterborne disease model of variable order which is analysed for the numerical computations for different variable orders. The results obtained for the variable orders have an advantage over the constant orders in that the variable order simulations present the fluctuation of the real dynamics throughout our observations of the simulations.

Suggested Citation

  • Hasib Khan & Jehad Alzabut & Haseena Gulzar & Osman Tunç & Sandra Pinelas, 2023. "On System of Variable Order Nonlinear p-Laplacian Fractional Differential Equations with Biological Application," Mathematics, MDPI, vol. 11(8), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1913-:d:1126651
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    References listed on IDEAS

    as
    1. Zareen A. Khan & Aziz Khan & Thabet Abdeljawad & Hasib Khan, 2022. "Computational Analysis Of Fractional Order Imperfect Testing Infection Disease Model," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-17, August.
    2. Bahaa, G.M., 2019. "Optimal control problem for variable-order fractional differential systems with time delay involving Atangana–Baleanu derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 129-142.
    3. Begum, Razia & Tunç, Osman & Khan, Hasib & Gulzar, Haseena & Khan, Aziz, 2021. "A fractional order Zika virus model with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    4. Sun, HongGuang & Chen, Wen & Chen, YangQuan, 2009. "Variable-order fractional differential operators in anomalous diffusion modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4586-4592.
    5. Zafar, Zain Ul Abadin & Zaib, Sumera & Hussain, Muhammad Tanveer & Tunç, Cemil & Javeed, Shumaila, 2022. "Analysis and numerical simulation of tuberculosis model using different fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    6. Devi, Amita & Kumar, Anoop, 2022. "Hyers–Ulam stability and existence of solution for hybrid fractional differential equation with p-Laplacian operator," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    7. F. A. Rihan & C. Tunc & S. H. Saker & S. Lakshmanan & R. Rakkiyappan, 2018. "Applications of Delay Differential Equations in Biological Systems," Complexity, Hindawi, vol. 2018, pages 1-3, September.
    8. Khan, Hasib & Jarad, Fahd & Abdeljawad, Thabet & Khan, Aziz, 2019. "A singular ABC-fractional differential equation with p-Laplacian operator," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 56-61.
    9. Solís-Pérez, J.E. & Gómez-Aguilar, J.F. & Atangana, A., 2018. "Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 175-185.
    10. Gómez-Aguilar, J.F., 2018. "Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 52-75.
    11. Sutar, Sagar T. & Kucche, Kishor D., 2021. "On Nonlinear Hybrid Fractional Differential Equations with Atangana-Baleanu-Caputo Derivative," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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    1. Khan, Hasib & Ahmed, Saim & Alzabut, Jehad & Azar, Ahmad Taher, 2023. "A generalized coupled system of fractional differential equations with application to finite time sliding mode control for Leukemia therapy," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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