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Approximate Analytical Solution For The Variable-Order Fractional Infectious Diseases Model

Author

Listed:
  • KHADIJA SHAHZADI

    (Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad 44000, Pakistan)

  • SYED ALI MOHSIN BUKHARI

    (Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad 44000, Pakistan†Space and Astrophysics Research Lab (SARL), National Centre of GIS and Space Applications (NCGSA), Institute of Space Technology, Islamabad 44000, Pakistan)

  • SHNO OTHMAN AHMED

    (��Department of Computer Science and Information Technology, College of Science, Salahaddin University-Erbil, Erbil, Kurdistan Region, Iraq)

  • FUAD A. AWWAD

    (�Department of Quantitative Analysis, College of Business Administration, King Saud University, P. O. Box 71115, Riyadh 11587, Saudi Arabia)

  • EMAD A. A. ISMAIL

    (�Department of Quantitative Analysis, College of Business Administration, King Saud University, P. O. Box 71115, Riyadh 11587, Saudi Arabia)

  • UMAIR ALI

    (Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad 44000, Pakistan)

  • HIJAZ AHMAD

    (�Institute of Research and Development, DuyTan University, Da Nang, Vietnam∥School of Engineering and Technology, DuyTan University, Da Nang, Vietnam**Department of Mathematics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu Seoul 02841, South Korea††Department of Technical Sciences, Western Caspian University, Baku 1001, Azerbaijan)

Abstract

In this paper, a nonlinear variable-order infectious diseases model is discussed and the derivative operator is in the Caputo sense for the range 0 < 𠜃(t) < 1. First, we used the Laplace transformation to the variable-order fractional derivatives and effectively transformed it into an integer-order derivative. Subsequently, the homotopy perturbation method (HPM) is used to obtain the semi-analytical solution of the nonlinear infectious diseases model. Ultimately, we showcase the effects of our new approximate solutions by presenting various graphical illustrations across various values for the relevant biological parameters. Our computation results are compared with existing solutions, and a close agreement is obtained demonstrating our approach’s accuracy and validity.

Suggested Citation

  • Khadija Shahzadi & Syed Ali Mohsin Bukhari & Shno Othman Ahmed & Fuad A. Awwad & Emad A. A. Ismail & Umair Ali & Hijaz Ahmad, 2025. "Approximate Analytical Solution For The Variable-Order Fractional Infectious Diseases Model," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(08), pages 1-13.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:08:n:s0218348x2540170x
    DOI: 10.1142/S0218348X2540170X
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