Browsing by Author "Khursheed J. Ansari"

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    A numerical scheme for fractional order mortgage model of economics
    (Elsevier B.V., 2023) Hafsa Naz; Thongchai Dumrongpokaphan; Thanin Sitthiwirattham; Hussam Alrabaiah; Khursheed J. Ansari; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th
    In this article, the famous mortgage model of economics is investigated by developing a numerical scheme. The considered model is proposed under the Caputo power law derivative of fractional order. Further, in the considered model by utilizing the time esteem of cash rule, we build up break even with vital and interest mortgage model that gives quickest installment plan with the least interest rate. The proposed scheme is based on some operational matrices of integration and differentiation of fractional order. For the required operational matrices, we use shifted Legendre polynomials. With the help of the operational matrices, we establish a numerical algorithm to convert the considered model to a system of Lyapunov matrix equation. By using Matlab, we then solve the resultant algebraic equation to get the required solution in numerical form. Further, we plot the approximate solution for various fractional order graphically. © 2023
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    Study of implicit-impulsive differential equations involving Caputo-Fabrizio fractional derivative
    (American Institute of Mathematical Sciences, 2022) Thanin Sitthiwirattham; Rozi Gul; Kamal Shah; Ibrahim Mahariq; Jarunee Soontharanon; Khursheed J. Ansari; K. Shah; Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, Pakistan; email: kamalshah408@gmail.com
    This article is devoted to investigate a class of non-local initial value problem of implicit-impulsive fractional differential equations (IFDEs) with the participation of the Caputo-Fabrizio fractional derivative (CFFD). By means of KrasnoselskiiÕs fixed-point theorem and BanachÕs contraction principle, the results of existence and uniqueness are obtained. Furthermore, we establish some results of Hyers-Ulam (H-U) and generalized Hyers-Ulam (g-H-U) stability. Finally, an example is provided to demonstrate our results. © 2022 the Author(s),.