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    Mathematical Evaluation and Dynamic Transmissions of a Cervical Cancer Model Using a Fractional Operator
    (Universal Wiser Publisher, 2024) Singh, Rakhi; Akguel, Ali; Mishra, Jyoti; Gupta, Vijay Kumar
    This scientific research investigates the fractional-order compartmental model of cervical cancer. The human papillomavirus (HPV) is responsible for the development of cervical cancer. The Caputo-Fabrizio fractional operator, which includes a section for treatment with antiretroviral drugs, is employed to examine this worldwide phenomenon. The mathematical model of cervical cancer that has been proposed recently is an extension of the integer-order model. The fractional derivative technique is a novel approach for these types of biological models. This paper employs fixed point theory to provide requirements for the existence, uniqueness, and stability of the fractional order cervical cancer model, utilizing the Caputo- Fabrizio operator. We have initially found an approximation solution to a proposed model via the iterative Laplace transform method, which is easily accessible. This approach integrates the Laplace transform technique with a reliable, novel iterative method. We evaluated parameters indicating the advancement of the illness and presented the numeric simulations. The observed outcomes indicate that a fractional factor has a crucial effect on controlling cervical cancer.
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    Öğe
    Mathematical Evaluation and Dynamic Transmissions of a Tumor Gr-owth Model Using a Generalized Singular and Non-Local Kernel
    (Universal Wiser Publisher, 2024) Singh, Rakhi; Mishra, Jyoti; Akgul, Ali; Gupta, Vijay Kumar
    Currently, fractional calculus plays a critical role in improving control techniques, analyzing disease transmission dynamics, and solving several other real-world problems. This research investigates the time-fractional tumor growth model using an innovative approach. The new modified fractional derivative operator employs a singular and non-local kernel, based on Atangana and Baleanu's concepts with the Caputo derivative. The tumor growth model used the newly modified fractional operator, which provided numerical simulation. With the introduction of this new operator, we provide significant analysis for the tumor growth epidemic model. We have proven the uniqueness and stability conditions of the model by utilizing Banach's fixed point theory and the Picard successive approximation method. Using the Laplace-Adomian decomposition method (LADM), we found the numerical solution to the Modified Atangana-Baleanu-Caputo derivative model. We have verified the convergence analysis of the suggested scheme. We ultimately utilize the suggested method to obtain numeric outcomes and simulations for the tumor growth model. The study investigates the effect of multiple biological variables on the transmission of tumor growth dynamics.