Browsing by Author "Arfan, Muhammad"

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A NEW NUMERICAL TREATMENT FOR FRACTIONAL DIFFERENTIAL EQUATIONS BASED ON NON-DISCRETIZATION OF DATA USING LAGUERRE POLYNOMIALS
(2020) Abdeljawad, Thabet; Jarad, Fahd; Arfan, Muhammad; Abdeljawad, Thabet; Jarad, Fahd; 234808
In this research work, we discuss an approximation techniques for boundary value problems (BVPs) of differential equations having fractional order (FODE). We avoid the method from discretization of data by applying polynomials of Laguerre and developed some matrices of operational types for the obtained numerical solution. By applying the operational matrices, the given problem is converted to some algebraic equation which on evaluation gives the required numerical results. These equations are of Sylvester types and can be solved by using matlab. We present some testing examples to ensure the correctness of the considered techniques.
Fractional Order Mathematical Model of Serial Killing with Different Choices of Control Strategy
(2022) Jarad, Fahd; Ahmad, Shabir; Arfan, Muhammad; Akgül, Ali; Jarad, Fahd; 234808
The current manuscript describes the dynamics of a fractional mathematical model of serial killing under the Mittag–Leffler kernel. Using the fixed point theory approach, we present a qualitative analysis of the problem and establish a result that ensures the existence of at least one solution. Ulam’s stability of the given model is presented by using nonlinear concepts. The iterative fractional-order Adams–Bashforth approach is being used to find the approximate solution. The suggested method is numerically simulated at various fractional orders. The simulation is carried out for various control strategies. Over time, all of the compartments demonstrate convergence and stability. Different fractional orders have produced an excellent comparison outcome, with low fractional orders achieving stability sooner.
Investigation of COVID-19 mathematical model under fractional order derivative
(2021) Baleanu, Dumitru; Arfan, Muhammad; Deebani, Wejdan; Shutaywi, Meshal; Baleanu, Dumitru; 56389
The given article is devoted to presentation of some results regarding existence and uniqueness of solution to a fractional order model that addressing the effect of immigration on the transmission dynamics of a population model. Further, in view of this investigation the effect of immigration have been checked on transmission of recent pandemic known as Corona virus COVID-19. The concerned results have been established by using fixed point theory approach. After investigation qualitative analysis of the considered model, by applying Laplace transform along with decomposition method, we have calculated some series type results for the concerned model. The unknown quantities of each equation have been decomposed into small quantities to calculate each small quantity very easily for the series solution by adding first few terms of the said quantities. Approximate results of some testing data with different cases are given to illustrate the results. © The authors. Published by EDP Sciences, 2021.