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Author: search.filters.author.Jeelani, Mdi Begum

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    Topological degree theory to investigate fractional order korteweg-de vries equation of porous media
    (2026-01-01)
    Ullah, Atta
    ;
    Khan, Zareen A.
    ;
    Fatima, Nahid
    ;
    Mlaiki, Nabil
    ;
    Jeelani, Mdi Begum
    The Korteweg-de Vries (KdV) equation is considered in this paper with fractional order derivative. We have considered the aforesaid equation under the non-singular derivative of fractional order introduced by Atangana-Baleanu-Caputo (ABC). We have implemented topological degree theory to deduce sufficient results for the existence and uniqueness of solution to the concerned problem. The concerned degree theory has been used to study a class of nonlinear integral equation. In this regard, we considered a general form for our proposed problem and then established appropriate conditions required for the existence and uniqueness of solution. Additionally, stability is an important requirement in investigating analytical or numerical solutions, therefore, we have attempted to derive some adequate results for the Hyers-Ulam-Type stability. Finally, for computing the approximate solution, we have used Laplace transform coupled with Adomian decomposition (LADM) to study the mentioned problem. Two concerted examples have been testified by the mentioned technique. Different surface plots have been presented to investigate the physical impact of fractional order, time and space variable on the propagation of wave solution.
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    FRACTIONAL-ORDER SENSITIVITY ANALYSIS OF LEPTOSPIROSIS TREATMENT DYNAMICS IN THE PRESENCE OF AN ENVIRONMENTAL BACTERIAL RESERVOIR WITH ARTIFICIAL NEURAL NETWORK SUPPORT
    (2026-01-01)
    Irshad, Ateeq Ur Rehman
    ;
    Ullah, Naeem
    ;
    Hassaballa, Abaker A.
    ;
    Jeelani, Mdi Begum
    ;
    Fatima, Nahid
    In this study, we develop and analyze a deterministic fractional-order human–animal–environment transmission model using the Caputo fractional-order derivative (CFOD) to investigate leptospirosis transmission dynamics, explicitly incorporating treatment for infected humans in the human population. The model accounts for indirect transmission through an environmental bacterial reservoir and shedding from infected animals. The qualitative features of the suggested model, such as positivity, boundedness, existence and uniqueness of solution, equilibrium points, and biological well-posedness of the solutions, are thoroughly demonstrated. The model captures nonlocal and memory-dependent characteristics that cannot be described by classical integer-order derivatives. The next-generation matrix (NGM) approach is used to determine the basic reproduction number (ℛ<inf>0</inf><sup>FV</sup>). The stability properties of the pathogen-extinction steady state and sustained-transmission steady state are investigated. In particular, Lyapunov function techniques are used to check the global stability of the PESS and STSS under suitable conditions, while Ulam–Hyers stability is established to examine the stability of the model solutions under small perturbations. To better understand the influence of model parameters, normalized forward sensitivity analysis is performed, showing that transmission, treatment, and recovery-related parameters exert the strongest influence on disease burden. Numerical simulations are used to verify theoretical results and investigate the effects of key epidemiological parameters on disease transmission. Finally, an artificial neural network (ANN) is employed only as a supplementary computational tool to reproduce the numerically obtained solution trajectories and to provide a consistency check of the computed results. The findings offer a valuable perspective on the dynamics of leptospirosis transmission and could inform disease control and intervention efforts.