Browsing by Author "Khalid, Aasma"

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Citation Count: Rashid, Saima;...et.al. (2022). "Fuzzy fractional estimates of Swift-Hohenberg model obtained using the Atangana-Baleanu fractional derivative operator", AIMS Mathematics, Vol.7, No.9, pp.16067-16101.
Fuzzy fractional estimates of Swift-Hohenberg model obtained using the Atangana-Baleanu fractional derivative operator
(2022) Rashid, Saima; Sultana, Sobia; Kanwal, Bushra; Jarad, Fahd; Khalid, Aasma; 234808
Swift-Hohenberg equations are frequently used to model the biological, physical and chemical processes that lead to pattern generation, and they can realistically represent the findings. This study evaluates the Elzaki Adomian decomposition method (EADM), which integrates a semi-analytical approach using a novel hybridized fuzzy integral transform and the Adomian decomposition method. Moreover, we employ this strategy to address the fractional-order Swift-Hohenberg model (SHM) assuming gH-differentiability by utilizing different initial requirements. The Elzaki transform is used to illustrate certain characteristics of the fuzzy Atangana-Baleanu operator in the Caputo framework. Furthermore, we determined the generic framework and analytical solutions by successfully testing cases in the series form of the systems under consideration. Using the synthesized strategy, we construct the approximate outcomes of the SHM with visualizations of the initial value issues by incorporating the fuzzy factor ϖ ∈ [0, 1] which encompasses the varying fractional values. Finally, the EADM is predicted to be effective and precise in generating the analytical results for dynamical fuzzy fractional partial differential equations that emerge in scientific disciplines.
Citation Count: Rashid, Saima;...et.al. (2022). "Novel numerical investigation of the fractional oncolytic effectiveness model with M1 virus via generalized fractional derivative with optimal criterion", Results in Physics, Vo.37.
Novel numerical investigation of the fractional oncolytic effectiveness model with M1 virus via generalized fractional derivative with optimal criterion
(2022) Rashid, Saima; Khalid, Aasma; Sultana, Sobia; Jarad, Fahd; Abualnaja, Khadijah M.; Hamed, Y.S.; 234808
Oncolytic virotherapy is an efficacious chemotherapeutic agent that addresses and eliminates cancerous tissues by employing recombinant infections. M1 is a spontaneously produced oncolytic alphavirus with exceptional specificity and powerful activity in individual malignancies. The objective of this paper is to develop and assess a novel fractional differential equation (FDEs)-based mathematical formalism that captures the mechanisms of oncogenic M1 immunotherapy. The aforesaid framework is demonstrated with the aid of persistence, originality, non-negativity, and stability of systems. Additionally, we also examine all conceivable steady states and the requirements that must exist for them to occur. We also investigate the global stability of these equilibria and the characteristics that induce them to be unstable. Furthermore, the Atangana–Baleanu fractional-order derivative is employed to generalize a treatment of the cancer model. This novel type of derivative furnishes us with vital understanding regarding parameters that are widely used in intricate mechanisms. The Picard–Lindelof approach is implemented to investigate the existence and uniqueness of solutions for the fractional cancer treatment system, and Picard's stability approach is used to address governing equations. The findings reveal that the system is more accurate when the fractional derivative is implemented, demonstrating that the behaviour of the cancer treatment can be interpreted when non-local phenomena are included in the system. Furthermore, numerical results for various configurations of the system are provided to exemplify the established simulation.
Citation Count: Khalid, Aasma...et al. (2019). "Numerical Solution of the Boundary Value Problems Arising in Magnetic Fields and Cylindrical Shells", Mathematics, Vol. 7, No. 6.
Numerical Solution of the Boundary Value Problems Arising in Magnetic Fields and Cylindrical Shells
(MDPI, 2019) Khalid, Aasma; Naeem, Muhammad Nawaz; Ullah, Zafar; Ghaffar, Abdul; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; (Al-Qurashi, Maysaa M.; 56389
This paper is devoted to the study of the Cubic B-splines to find the numerical solution of linear and non-linear 8th order BVPs that arises in the study of astrophysics, magnetic fields, astronomy, beam theory, cylindrical shells, hydrodynamics and hydro-magnetic stability, engineering, applied physics, fluid dynamics, and applied mathematics. The recommended method transforms the boundary problem to a system of linear equations. The algorithm we are going to develop in this paper is not only simply the approximation solution of the 8th order BVPs using Cubic-B spline but it also describes the estimated derivatives of 1st order to 8th order of the analytic solution. The strategy is effectively applied to numerical examples and the outcomes are compared with the existing results. The method proposed in this paper provides better approximations to the exact solution.
Citation Count: Chu, Yu-Ming;...et.al. (2023). "Predictive dynamical modeling and stability of the equilibria in a discrete fractional difference COVID-19 epidemic model", Results in Physics, Vol.49.
Predictive dynamical modeling and stability of the equilibria in a discrete fractional difference COVID-19 epidemic model
(2023) Chu, Yu-Ming; Rashid, Saima; Akdemir, Ahmet Ocak; Khalid, Aasma; Baleanu, Dumitru; Al-Sinan, Bushra R.; Elzibar, O. A. I.; 56389
The SARSCoV-2 virus, also known as the coronavirus-2, is the consequence of COVID-19, a severe acute respiratory syndrome. Droplets from an infectious individual are how the pathogen is transmitted from one individual to another and occasionally, these particles can contain toxic textures that could also serve as an entry point for the pathogen. We formed a discrete fractional-order COVID-19 framework for this investigation using information and inferences from Thailand. To combat the illnesses, the region has implemented mandatory vaccination, interpersonal stratification and mask distribution programs. As a result, we divided the vulnerable people into two groups: those who support the initiatives and those who do not take the influence regulations seriously. We analyze endemic problems and common data while demonstrating the threshold evolution defined by the fundamental reproductive quantity R0. Employing the mean general interval, we have evaluated the configuration value systems in our framework. Such a framework has been shown to be adaptable to changing pathogen populations over time. The Picard Lindelof technique is applied to determine the existence-uniqueness of the solution for the proposed scheme. In light of the relationship between the R0 and the consistency of the fixed points in this framework, several theoretical conclusions are made. Numerous numerical simulations are conducted to validate the outcome.
Citation Count: Khalid, Aasma...et al.(2021). "Solutions of BVPs arising in hydrodynamic and magnetohydro-dynamic stability theory using polynomial and non-polynomial splines", Alexandria Engineering Journal, Vol. 60, No. 1, pp. 941-953.
Solutions of BVPs arising in hydrodynamic and magnetohydro-dynamic stability theory using polynomial and non-polynomial splines
(2021) Khalid, Aasma; Ghaffar, Abdul; Naeem, M. Nawaz; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
This paper describes the exceptionally precise results of 6th-order and 8th-order nonlinear boundary-value problems(BVPs). Cubic-Nonpolynomial spline(CNPS) and Cubic-polynomial spline(CNPS) are utilized to solve such types of BVPs. We develop the class of numerical techniques for a particular selection of the factors that are associated with nonpolynomial and polynomial splines. Using the developed class of numerical techniques, the problem is reduced to a new system that consists of 2nd-order BVPs only. The end conditions associated with the BVPs are determined. For each problem, the results obtained by CNPS and CPS is compared with the exact solution. The absolute error(AE) for every iteration is calculated. To show that the suitable responses established by using CNPS and CPS have a higher level of preciseness, the absolute errors of the CNPS and CPS have been compared with different techniques such as DTM, ADM, Parametric septic splines, Variational-iteration method(VIM), Daftardar Jafari strategy, MDM, Cubic B-Spline, Homotopy method(HM), Quintic and Sextic B-spline and observed to be more accurate. Graphs that describe the graphical comparison of CNPS and CPS at n=10 are also included in this paper.