Yazar "Ahmed, Idris" seçeneğine göre listele

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    Öğe
    A Caputo-Fabrizio fractional-order cholera model and its sensitivity analysis
    (2023) Ahmed, Idris; Akgül, Ali; Jarad, Fahd; Kumam, Poom; Nonlaopon, Kamsing
    In recent years, the availability of advanced computational techniques has led to a growing emphasis on fractional-order derivatives. This development has enabled researchers to explore the intricate dynamics of various biological models by employing fractional-order derivatives instead of traditional integer-order derivatives. This paper proposes a Caputo-Fabrizio fractional-order cholera epidemic model. Fixed-point theorems are utilized to investigate the existence and uniqueness of solutions. A recent and effective numerical scheme is employed to demonstrate the model's complex behaviors and highlight the advantages of fractional-order derivatives. Additionally, a sensitivity analysis is conducted to identify the most influential parameters.
  • [ X ]
    Öğe
    On ?-Hilfer generalized proportional fractional operators
    (Amer Inst Mathematical Sciences-Aims, 2021) Mallah, Ishfaq; Ahmed, Idris; Akgul, Ali; Jarad, Fahd; Alha, Subhash
    In this paper, we introduce a generalized fractional operator in the setting of Hilfer fractional derivatives, the psi-Hilfer generalized proportional fractional derivative of a function with respect to another function. The proposed operator can be viewed as an interpolator between the Riemann-Liouville and Caputo generalized proportional fractional operators. The properties of the proposed operator are established under some classical and standard assumptions. As an application, we formulate a nonlinear fractional differential equation with a nonlocal initial condition and investigate its equivalence with Volterra integral equations, existence, and uniqueness of solutions. Finally, illustrative examples are given to demonstrate the theoretical results.