Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Author: search.filters.author.Javeed, ShumailaWoS Q: search.filters.wosQuartile.Q3

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  • Article
    Citation - WoS: 1
    Citation - Scopus: 4
    Fractional Modeling of Cancer With Mixed Therapies
    (Imr Press, 2023) Ul Abdeen, Zain; Baleanu, Dumitru; Javeed, Shumaila
    Background: Cancer is the biggest cause of mortality globally, with approximately 10 million fatalities expected by 2020, or about one in every six deaths. Breast, lung, colon, rectum, and prostate cancers are the most prevalent types of cancer. Methods: In this work, fractional modeling is presented which describes the dynamics of cancer treatment with mixed therapies (immunotherapy and chemotherapy). Mathematical models of cancer treatment are important to understand the dynamical behavior of the disease. Fractional models are studied considering immunotherapy and chemotherapy to control cancer growth at the level of cell populations. The models consist of the system of fractional differential equations (FDEs). Fractional term is defined by Caputo fractional derivative. The models are solved numerically by using Adams-Bashforth-Moulton method. Results: For all fractional models the reasonable range of fractional order is between beta = 0.6 and beta = 0.9. The equilibrium points and stability analysis are presented. Moreover, positivity and boundedness of the solution are proved. Furthermore, a graphical representation of cancerous cells, immunotherapy and chemotherapy is presented to understand the behaviour of cancer treatment. Conclusions: At the end, a curve fitting procedure is presented which may help medical practitioners to treat cancer patients.
  • Article
    Citation - WoS: 33
    Citation - Scopus: 34
    Application of Modified Extended Tanh Technique for Solving Complex Ginzburg-Landau Equation Considering Kerr Law Nonlinearity
    (Tech Science Press, 2021) Shallal, Muhannad A.; Mirhosseini-Alizamini, Seyed Mehdi; Rezazadeh, Hadi; Javeed, Shumaila; Baleanu, Dumitru; Chu, Yuming
    The purpose of this work is to find new soliton solutions of the complex Ginzburg-Landau equation (GLE) with Kerr law non-linearity. The considered equation is an imperative nonlinear partial differential equation (PDE) in the field of physics. The applications of complex GLE can be found in optics, plasma and other related fields. The modified extended tanh technique with Riccati equation is applied to solve the Complex GLE. The results are presented under a suitable choice for the values of parameters. Figures are shown using the three and two-dimensional plots to represent the shape of the solution in real, and imaginary parts in order to discuss the similarities and difference between them. The graphical representation of the results depicts the typical behavior of soliton solutions. The obtained soliton solutions are of different forms, such as, hyperbolic and trigonometric functions. The results presented in this paper are novel and reported first time in the literature. Simulation results establish the validity and applicability of the suggested technique for the complex GLE. The suggested method with symbolic computational software such as, Mathematica and Maple, is proven as an effective way to acquire the soliton solutions of nonlinear partial differential equations (PDEs) as well as complex PDEs.