Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Publisher: search.filters.publisher.Amer inst Mathematical Sciences-aimsSubject: search.filters.subject.Existence And Uniqueness

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  • Article
    Citation - WoS: 12
    Citation - Scopus: 11
    A Computational Study of a Stochastic Fractal-Fractional Hepatitis B Virus Infection Incorporating Delayed Immune Reactions Via the Exponential Decay
    (Amer inst Mathematical Sciences-aims, 2022) Rashid, Saima; Jarad, Fahd; Al Qurashi, Maysaa
    Recently, researchers have become interested in modelling, monitoring, and treatment of hepatitis B virus infection. Understanding the various connections between pathogens, immune systems, and general liver function is crucial. In this study, we propose a higher-order stochastically modified delay differential model for the evolution of hepatitis B virus transmission involving defensive cells. Taking into account environmental stimuli and ambiguities, we presented numerical solutions of the fractal-fractional hepatitis B virus model based on the exponential decay kernel that reviewed the hepatitis B virus immune system involving cytotoxic T lymphocyte immunological mechanisms. Furthermore, qualitative aspects of the system are analyzed such as the existence-uniqueness of the non-negative solution, where the infection endures stochastically as a result of the solution evolving within the predetermined system's equilibrium state. In certain settings, infection-free can be determined, where the illness settles down tremendously with unit probability. To predict the viability of the fractal-fractional derivative outcomes, a novel numerical approach is used, resulting in several remarkable modelling results, including a change in fractional-order delta with constant fractal-dimension pi, delta with changing pi, and delta with changing both delta and pi. White noise concentration has a significant impact on how bacterial infections are treated.
  • Article
    Citation - WoS: 30
    On Ψ-Hilfer Generalized Proportional Fractional Operators
    (Amer inst Mathematical Sciences-aims, 2021) Ahmed, Idris; Akgul, Ali; Jarad, Fahd; Alha, Subhash; Mallah, Ishfaq
    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.