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Browsing by Author "Khan, Muhammad Altaf"

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    Citation - WoS: 95
    Citation - Scopus: 108
    A Fractional Model for the Dynamics of Tuberculosis Infection Using Caputo-Fabrizio Derivative
    (Amer inst Mathematical Sciences-aims, 2020) Ullah, Saif; Baleanu, Dumitru; Khan, Muhammad Altaf; Farooq, Muhammad; Hammouch, Zakia; Baleanu, Dumitru; 56389; Matematik
    In the present paper, we study the dynamics of tuberculosis model using fractional order derivative in Caputo-Fabrizio sense. The number of confirmed notified cases reported by national TB program Khyber Pakhtunkhwa, Pakistan, from the year 2002 to 2017 are used for our analysis and estimation of the model biological parameters. The threshold quantity R-0 and equilibria of the model are determined. We prove the existence of the solution via fixed-point theory and further examine the uniqueness of the model variables. An iterative solution of the model is computed using fractional Adams-Bashforth technique. Finally, the numerical results are presented by using the estimated values of model parameters to justify the significance of the arbitrary fractional order derivative. The graphical results show that the fractional model of TB in Caputo-Fabrizio sense gives useful information about the complexity of the model and one can get reliable information about the model at any integer or non-integer case.
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    Citation - WoS: 121
    Citation - Scopus: 134
    Modeling The Dynamics of Hepatitis E Via The Caputo-Fabrizio Derivative
    (Edp Sciences S A, 2019) Khan, Muhammad Altaf; Baleanu, Dumitru; Hammouch, Zakia; Baleanu, Dumitru; 56389; Matematik
    A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics. Therefore, the present work explores the HEV dynamics in fractional derivative. The Caputo-Fabriizo derivative is used to study the dynamics of HEV. First, the essential properties of the model will be presented and then describe the HEV model with CF derivative. Application of fixed point theory is used to obtain the existence and uniqueness results associated to the model. By using Adams-Bashfirth numerical scheme the solution is obtained. Some numerical results and tables for arbitrary order derivative are presented.