WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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Author: search.filters.author.Al Qurashi, MaysaaLanguage: search.filters.language.en

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Now showing 1 - 10 of 18
  • Article
    Citation - WoS: 8
    Citation - Scopus: 10
    Fractional-Order Partial Differential Equations Describing Propagation of Shallow Water Waves Depending on Power and Mittag-Leffier Memory
    (Amer inst Mathematical Sciences-aims, 2022) Rashid, Saima; Sultana, Sobia; Jarad, Fahd; Alsharif, Abdullah M.; Al Qurashi, Maysaa
    In this research, the (q) over bar -homotopy analysis transform method ((q) over bar -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) over bar -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.
  • Article
    Citation - WoS: 12
    Citation - Scopus: 11
    A Computational Study of a Stochastic Fractal-Fractional Hepatitis B Virus Infection Incorporating Delayed Immune Reactions Via the Exponential Decay
    (Amer inst Mathematical Sciences-aims, 2022) Rashid, Saima; Jarad, Fahd; Al Qurashi, Maysaa
    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 delta with constant fractal-dimension pi, delta with changing pi, and delta with changing both delta and pi. White noise concentration has a significant impact on how bacterial infections are treated.
  • Article
    Citation - WoS: 17
    Citation - Scopus: 19
    New Numerical Dynamics of the Fractional Monkeypox Virus Model Transmission Pertaining To Nonsingular Kernels
    (Amer inst Mathematical Sciences-aims, 2023) Rashid, Saima; Alshehri, Ahmed M.; Jarad, Fahd; Safdar, Farhat; Al Qurashi, Maysaa; Qurashi, Maysaa Al
    Monkeypox (MPX) is a zoonotic illness that is analogous to smallpox. Monkeypox infections have moved across the forests of Central Africa, where they were first discovered, to other parts of the world. It is transmitted by the monkeypox virus, which is a member of the Poxviridae species and belongs to the Orthopoxvirus genus. In this article, the monkeypox virus is investigated using a deterministic mathematical framework within the Atangana-Baleanu fractional derivative that depends on the generalized Mittag-Leffler (GML) kernel. The system's equilibrium conditions are investigated and examined for robustness. The global stability of the endemic equilibrium is addressed using Jacobian matrix techniques and the Routh-Hurwitz threshold. Furthermore, we also identify a criterion wherein the system's disease-free equilibrium is globally asymptotically stable. Also, we employ a new approach by combining the two-step Lagrange polynomial and the fundamental concept of fractional calculus. The numerical simulations for multiple fractional orders reveal that as the fractional order reduces from 1, the virus's transmission declines. The analysis results show that the proposed strategy is successful at reducing the number of occurrences in multiple groups. It is evident that the findings suggest that isolating affected people from the general community can assist in limiting the transmission of pathogens.
  • Article
    Citation - WoS: 28
    Citation - Scopus: 29
    Solitons and Jacobi Elliptic Function Solutions To the Complex Ginzburg-Landau Equation
    (Frontiers Media Sa, 2020) Hosseini, Kamyar; Mirzazadeh, Mohammad; Osman, M. S.; Al Qurashi, Maysaa; Baleanu, Dumitru
    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.
  • Article
    Citation - WoS: 89
    A Modified Analytical Approach With Existence and Uniqueness for Fractional Cauchy Reaction-Diffusion Equations
    (Springer, 2020) Kumar, Amit; Abbas, Syed; Al Qurashi, Maysaa; Baleanu, Dumitru; Kumar, Sunil
    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.
  • Erratum
    Citation - WoS: 4
    Citation - Scopus: 8
    Retracted: an Analytical Investigation of Fractional-Order Biological Model Using an Innovative Technique (Retracted Article)
    (Wiley-hindawi, 2020) Khan, Adnan; Al Qurashi, Maysaa; Baleanu, Dumitru; Shah, Rasool; Khan, Hassan
    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.
  • Article
    Citation - WoS: 41
    Citation - Scopus: 47
    An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems
    (Mdpi, 2020) Khan, Adnan; Ali, Izaz; Al Qurashi, Maysaa; Khan, Hassan; Shah, Rasool; Baleanu, Dumitru; Qin, Ya; Qurashi, Maysaa Al
    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.
  • Article
    Citation - WoS: 13
    Citation - Scopus: 30
    Some Fractional Calculus Findings Associated With the Incomplete I-Functions
    (Springer, 2020) Bhatter, Sanjay; Meena, Sapna; Baleanu, Dumitru; Al Qurashi, Maysaa; Purohit, Sunil Dutt; Jangid, Kamlesh
    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.
  • Article
    Citation - WoS: 27
    Citation - Scopus: 50
    Approximate Analytical Solutions of Goursat Problem Within Local Fractional Operators
    (int Scientific Research Publications, 2016) Jassim, Hassan Kamil; Al Qurashi, Maysaa; Baleanu, Dumitru
    The local fractional differential transform method (LFDTM) and local fractional decomposition method (LFDM) are applied to implement the homogeneous and nonhomogeneous Goursat problem involving local fractional derivative operators. The approximate analytical solution of this problem is calculated in form of a series with easily computable components. Examples are studied in order to show the accuracy and reliability of presented methods. We demonstrate that the two approaches are very effective and convenient for finding the analytical solutions of partial differential equations with local fractional derivative operators. (C) 2016 All rights reserved.
  • Article
    Citation - WoS: 88
    The Extended Mittag-Leffler Function Via Fractional Calculus
    (int Scientific Research Publications, 2017) Baleanu, Dumitru; Al Qurashi, Maysaa; Purohit, Sunil Dutt; Mubeen, Shahid; Arshad, Muhammad; Rahman, Gauhar
    In this study, our main attempt is to introduce fractional calculus (fractional integral and differential) operators which contain the following new family of extended Mittag-Leffler function: E-alpha,beta(gamma;q,c) (z) = Sigma(infinity)(n=0) B-p (gamma + nq, c - gamma)(c)(nq) z(n)/B(gamma, c - gamma)Gamma(alpha n + beta) n!' (z,beta,gamma is an element of C), as its kernel. We also investigate a certain number of their consequences containing the said function in their kernels. (C) 2017 All rights reserved.