Browsing by Author "Hasib Khan"

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    A new study on the existence and stability to a system of coupled higher-order nonlinear BVP of hybrid FDEs under the p-Laplacian operator
    (American Institute of Mathematical Sciences, 2022) Abdulwasea Alkhazzan; Wadhah Al-Sadi; Varaporn Wattanakejorn; Hasib Khan; Thanin Sitthiwirattham; Sina Etemad; Shahram Rezapour; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th; S. Rezapour; Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran; email: sh.rezapour@azaruniv.ac.ir
    In this paper, we study a general system of fractional hybrid differential equations with a nonlinear _p-operator, and prove the existence of solution, uniqueness of solution and Hyers-Ulam stability. We use the Caputo fractional derivative in this system so that our system is more general and complex than other nonlinear systems studied before. To establish the results, Green functions are used to transform the considered hybrid boundary problem into a system of fractional integral equations. Then, with the help of the topological degree theorem, we derive some sufficient conditions that ensure the existence and uniqueness of solutions for the proposed system. Finally, an example is presented to show the validity and correctness of the obtained results. © 2022 the Author(s), licensee AIMS Press.
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    Investigation of the stochastic modeling of covid-19 with environmental noise from the analytical and numerical point of view
    (MDPI, 2021) Shah Hussain; Elissa Nadia Madi; Hasib Khan; Sina Etemad; Shahram Rezapour; Thanin Sitthiwirattham; Nichaphat Patanarapeelert; S. Rezapour; Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, 53751-71379, Iran; email: sh.rezapour@azaruniv.ac.ir; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th; N. Patanarapeelert; Department of Mathematics, Faculty of Applied Science, King MongkutÕs University of Technology North Bangkok, Bangkok, 10800, Thailand; email: nichaphat.p@sci.kmutnb.ac.th
    In this article, we propose a novel mathematical model for the spread of COVID-19 involving environmental white noise. The new stochastic model was studied for the existence and persistence of the disease, as well as the extinction of the disease. We noticed that the existence and extinction of the disease are dependent on R0 (the reproduction number). Then, a numerical scheme was developed for the computational analysis of the model; with the existing values of the parameters in the literature, we obtained the related simulations, which gave us more realistic numerical data for the future prediction. The mentioned stochastic model was analyzed for different values of s1, s2 and b1, b2, and both the stochastic and the deterministic models were compared for the future prediction of the spread of COVID-19. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.