Browsing by Author "Salih Djilali"

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    Analysis of a discrete mathematical COVID-19 model
    (Elsevier B.V., 2021) Thanin Sitthiwirattham; Anwar Zeb; Saowaluck Chasreechai; Zohreh Eskandari; Mouhcine Tilioua; Salih Djilali; S. Djilali; Department of Mathematics, Faculty of Exact Sciences and Computer Science, Hassiba Benbouali University, Chlef, Algeria; email: s.djilali@univ-chlef.dz
    To describe the main propagation of the COVID-19 and has to find the control for the rapid spread of this viral disease in real life, in current manuscript a discrete form of the SEIR model is discussed. The main aim of this is to describe the viral disease in simplest way and the basic properties that are related with the nature of curves for susceptible and infected individuals are discussed here. The elementary numerical examples are given by using the real data of India and Algeria. © 2021 The Author(s)
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    COVID-19 MODELLING WITH SQUARE ROOT SUSCEPTIBLE-INFECTED INTERACTION
    (Serbian Society of Heat Transfer Engineers, 2023) Nadia Gul; Anwar Zeb; Salih Djilali; Mazz Ullah; Zohreh Eskandari; Thitiporn Linitda; A. Zeb; Department of Mathematics, COMSATS University Islamabad, Abbottabad, Pakistan; email: thitiporn_lin@dusit.ac.th; T. Linitda; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, Thailand; email: anwar@cuiatd.edu.pk
    We propose a COVID-19 mathematical model related to functional shape with square root susceptible-infected interaction. Using the Hurwitz criterion and then a graph theoretical-method for the construction of a Lyapunov function, we discuss both local and global stability. The analytical solution of the system is obtained in a special case. A non-standard finite difference scheme is then developed with the aim to obtain a proper discrete-time version of the model. Simulations show a good agreement between the proposed discretization and the results given by standard numerical methods. © 2023 Society of Thermal Engineers of Serbia Published by the Vin_a Institute of Nuclear Sciences, Belgrade, Serbia. This is an open access article distributed under the CC BY-NC-ND 4.0 terms and conditions
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    Semi-analytical solutions for fuzzy caputoÐfabrizio fractional-order two-dimensional heat equation
    (MDPI, 2021) Thanin Sitthiwirattham; Muhammad Arfan; Kamal Shah; Anwar Zeb; Salih Djilali; Saowaluck Chasreechai; A. Zeb; Department of Mathematics, Abbotabad Campus, COMSATS University of Islamabad, Khyber Pakhtunkhwa, 22060, Pakistan; email: anwar@cuiatd.edu.pk
    In the analysis in this article, we developed a scheme for the computation of a semi-analytical solution to a fuzzy fractional-order heat equation of two dimensions having some external diffusion source term. For this, we applied the Laplace transform along with decomposition tech-niques and the Adomian polynomial under the CaputoÐFabrizio fractional differential operator. Furthermore, for obtaining a semi-analytical series-type solution, the decomposition of the unknown quantity and its addition established the said solution. The obtained series solution was calculated and approached the approximate solution of the proposed equation. For the validation of our scheme, three different examples have been provided, and the solutions were calculated in fuzzy form. All the three illustrations simulated two different fractional orders between 0 and 1 for the upper and lower portions of the fuzzy solution. The said fractional operator is nonsingular and global due to the presence of the exponential function. It globalizes the dynamical behavior of the said equation, which is guaranteed for all types of fuzzy solution lying between 0 and 1 at any fractional order. The fuzziness is also included in the unknown quantity due to the fuzzy number providing the solution in fuzzy form, having upper and lower branches. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.