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Stability analysis for fractional order advection–reaction diffusion system

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  • Khan, Hasib
  • Gómez-Aguilar, J.F.
  • Khan, Aziz
  • Khan, Tahir Saeed

Abstract

In this paper, we present an alternative representation of the advection–reaction diffusion model involving fractional-order derivatives with Mittag-Leffler kernel. The study includes three main aspects: existence and uniqueness of solutions, Hyers–Ulam stability, and numerical simulations. For the existence and uniqueness of solutions, we use fixed point approach; also, we presents the Hyers–Ulam stability. For the numerical simulations, a new numerical scheme that involve Lagrange interpolation, Laplace transform and forward Euler technique is considered. Numerical simulations were obtained for some specific parameters.

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  • Khan, Hasib & Gómez-Aguilar, J.F. & Khan, Aziz & Khan, Tahir Saeed, 2019. "Stability analysis for fractional order advection–reaction diffusion system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 737-751.
    • Handle: RePEc:eee:phsmap:v:521:y:2019:i:c:p:737-751
    DOI: 10.1016/j.physa.2019.01.102
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    References listed on IDEAS

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    Cited by:

    1. Ndivhuwo Ndou & Phumlani Dlamini & Byron Alexander Jacobs, 2022. "Enhanced Unconditionally Positive Finite Difference Method for Advection–Diffusion–Reaction Equations," Mathematics, MDPI, vol. 10(15), pages 1-18, July.
    2. Ayesha Javed & Syed Asad Ali Gillani & Wasim Abbass & Muhammad Rizwan Riaz & Rashid Hameed & Safeer Abbas & Abdelatif Salmi & Ahmed Farouk Deifalla, 2022. "Mechanical Performance of Amorphous Metallic Fiber-Reinforced and Rubberized Thin Bonded Cement-Based Overlays," Sustainability, MDPI, vol. 14(13), pages 1-22, July.
    3. Kumar, Surendra & Sharma, Abhishek & Pal Singh, Harendra, 2021. "Convergence and global stability analysis of fractional delay block boundary value methods for fractional differential equations with delay," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    4. 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.
    5. Ali, Zeeshan & Rabiei, Faranak & Hosseini, Kamyar, 2023. "A fractal–fractional-order modified Predator–Prey mathematical model with immigrations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 466-481.

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