Browsing by Author "Al Qurashi, Maysaa"

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Citation Count: Al Qurashi, Maysaa; Rashid, Saima; Jarad, Fahd. (2022). "A computational study of a stochastic fractal-fractional hepatitis B virus infection incorporating delayed immune reactions via the exponential decay", Mathematical Biosciences and Engineering, Vol.19, No.12, pp.12950-12980.
A computational study of a stochastic fractal-fractional hepatitis B virus infection incorporating delayed immune reactions via the exponential decay
(2022) Al Qurashi, Maysaa; Rashid, Saima; Jarad, Fahd; 234808
Recently, researchers have become interested in modelling, monitoring, and treatment of hepatitis B virus infection. Understanding the various connections between pathogens, immune systems, and general liver function is crucial. In this study, we propose a higher-order stochastically modified delay differential model for the evolution of hepatitis B virus transmission involving defensive cells. Taking into account environmental stimuli and ambiguities, we presented numerical solutions of the fractal-fractional hepatitis B virus model based on the exponential decay kernel that reviewed the hepatitis B virus immune system involving cytotoxic T lymphocyte immunological mechanisms. Furthermore, qualitative aspects of the system are analyzed such as the existence-uniqueness of the non-negative solution, where the infection endures stochastically as a result of the solution evolving within the predetermined system’s equilibrium state. In certain settings, infection-free can be determined, where the illness settles down tremendously with unit probability. To predict the viability of the fractal-fractional derivative outcomes, a novel numerical approach is used, resulting in several remarkable modelling results, including a change in fractional-order δ with constant fractal-dimension $, δ with changing $, and δ with changing both δ and $. White noise concentration has a significant impact on how bacterial infections are treated.
Citation Count: Kumar, Sunil...et al. (2020). "A modified analytical approach with existence and uniqueness for fractional Cauchy reaction-diffusion equations", Advances in Difference Equations, Vol. 2020, No. 1.
A modified analytical approach with existence and uniqueness for fractional Cauchy reaction-diffusion equations
(2020) Kumar, Sunil; Kumar, Amit; Abbas, Syed; Al Qurashi, Maysaa; Baleanu, Dumitru; 56389
This article mainly explores and applies a modified form of the analytical method, namely the homotopy analysis transform method (HATM) for solving time-fractional Cauchy reaction-diffusion equations (TFCRDEs). Then mainly we address the error norms L2 and L infinity for a convergence study of the proposed method. We also find existence, uniqueness and convergence in the analysis for TFCRDEs. The projected method is illustrated by solving some numerical examples. The obtained numerical solutions by the HATM method show that it is simple to employ. An excellent conformity obtained between the solution got by the HATM method and the various well-known results available in the current literature. Also the existence and uniqueness of the solution have been demonstrated.
Citation Count: Khan, Hassan...et al. (2020). "An Analytical Investigation of Fractional-Order Biological Model Using an Innovative Technique", Complexity, Vol. 2020.
An Analytical Investigation of Fractional-Order Biological Model Using an Innovative Technique
(2020) Khan, Hassan; Khan, Adnan; Al Qurashi, Maysaa; Baleanu, Dumitru; Shah, Rasool; 56389
In this paper, a new so-called iterative Laplace transform method is implemented to investigate the solution of certain important population models of noninteger order. The iterative procedure is combined effectively with Laplace transformation to develop the suggested methodology. The Caputo operator is applied to express the noninteger derivative of fractional order. The series form solution is obtained having components of convergent behavior toward the exact solution. For justification and verification of the present method, some illustrative examples are discussed. The closed contact is observed between the obtained and exact solutions. Moreover, the suggested method has a small volume of calculations; therefore, it can be applied to handle the solutions of various problems with fractional-order derivatives.
Citation Count: Qin, Ya...et al. (2020). "An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems", Energies, Vol. 13, No. 11.
An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems
(2020) Qin, Ya; Khan, Adnan; Ali, Izaz; Al Qurashi, Maysaa; Khan, Hassan; Shah, Rasool; Baleanu, Dumitru; 56389
Mostly, it is very difficult to obtained the exact solution of fractional-order partial differential equations. However, semi-analytical or numerical methods are considered to be an alternative to handle the solutions of such complicated problems. To extend this idea, we used semi-analytical procedures which are mixtures of Laplace transform, Shehu transform and Homotopy perturbation techniques to solve certain systems with Caputo derivative differential equations. The effectiveness of the present technique is justified by taking some examples. The graphical representation of the obtained results have confirmed the significant association between the actual and derived solutions. It is also shown that the suggested method provides a higher rate of convergence with a very small number of calculations. The problems with derivatives of fractional-order are also solved by using the present method. The convergence behavior of the fractional-order solutions to an integer-order solution is observed. The convergence phenomena described a very broad concept of the physical problems. Due to simple and useful implementation, the current methods can be used to solve problems containing the derivative of a fractional-order.
Citation Count: Al Qurashi, Maysaa;...et.al. (2022). "Fractional-order partial differential equations describing propagation of shallow water waves depending on power and Mittag-Leffler memory", AIMS Mathematics, Vol.7, No.7, pp. 12587-12619.
Fractional-order partial differential equations describing propagation of shallow water waves depending on power and Mittag-Leffler memory
(2022) Al Qurashi, Maysaa; Rashid, Saima; Sultana, Sobia; Jarad, Fahd; Alsharif, Abdullah M.; 234808
In this research, the ¯q-homotopy analysis transform method (¯q-HATM) is employed to identify fractional-order Whitham–Broer–Kaup equation (WBKE) solutions. The WBKE is extensively employed to examine tsunami waves. With the aid of Caputo and Atangana-Baleanu fractional derivative operators, to obtain the analytical findings of WBKE, the predicted algorithm employs a combination of ¯q-HAM and the Aboodh transform. The fractional operators are applied in this work to show how important they are in generalizing the frameworks connected with kernels of singularity and non-singularity. To demonstrate the applicability of the suggested methodology, various relevant problems are solved. Graphical and tabular results are used to display and assess the findings of the suggested approach. In addition, the findings of our recommended approach were analyzed in relation to existing methods. The projected approach has fewer processing requirements and a better accuracy rate. Ultimately, the obtained results reveal that the improved strategy is both trustworthy and meticulous when it comes to assessing the influence of nonlinear systems of both integer and fractional order.
Citation Count: Hosseini, Kamyar...et al. (2020). "Solitons and Jacobi Elliptic Function Solutions to the Complex Ginzburg–Landau Equation", Frontiers in Physics, Vol. 8.
Solitons and Jacobi Elliptic Function Solutions to the Complex Ginzburg–Landau Equation
(2020) Hosseini, Kamyar; Mirzazadeh, Mohammad; Osman, M.S.; Al Qurashi, Maysaa; Baleanu, Dumitru; 56389
The complex Ginzburg–Landau (CGL) equation which describes the soliton propagation in the presence of the detuning factor is firstly considered; then its solitons as well as Jacobi elliptic function solutions are obtained systematically using a modified Jacobi elliptic expansion method. In special cases, several dark and bright soliton solutions to the CGL equation are retrieved when the modulus of ellipticity approaches unity. The results presented in the current work can help to complete previous studies on the complex Ginzburg–Landau equation.
Citation Count: Jangid, Kamlesh...et al. (2020). "Some fractional calculus findings associated with the incomplete I-functions", Advances in Difference Equations, vol. 2020, No. 1.
Some fractional calculus findings associated with the incomplete I-functions
(2020) Jangid, Kamlesh; Bhatter, Sanjay; Meena, Sapna; Baleanu, Dumitru; Al Qurashi, Maysaa; Purohit, Sunil Dutt; 56389
In this article, several interesting properties of the incomplete I-functions associated with the Marichev-Saigo-Maeda (MSM) fractional operators are studied and investigated. It is presented that the order of the incomplete I-functions increases about the utilization of the above-mentioned operators toward the power multiple of the incomplete I-functions. Further, the Caputo-type MSM fractional order differentiation for the incomplete I-functions is studied and investigated. Saigo, Riemann-Liouville, and Erdelyi-Kober fractional operators are also discussed as specific cases.