Matematik Bölümü Yayın Koleksiyonu

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

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Scopus Q: search.filters.scopusQuartile.Q2Subject: search.filters.subject.Fractional Differential Equation

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Now showing 1 - 5 of 5
  • Article
    Citation - WoS: 34
    Citation - Scopus: 36
    Exact Solutions of Boussinesq and Kdv-Mkdv Equations by Fractional Sub-Equation Method
    (Editura Acad Romane, 2013) Jafari, Hossein; Baleanu, Dumitru; Tajadodi, Haleh; Baleanu, Dumitru; Al-Zahrani, Abdulrahim A.; Alhamed, Yahia A.; Zahid, Adnan H.; Matematik
    A fractional sub-equation method is introduced to solve fractional differential equations. By the aid of the solutions of the fractional Riccati equation, we construct solutions of the Boussinesq and KdV-mKdV equations of fractional order. The obtained results show that this method is very efficient and easy to apply for solving fractional partial differential equations.
  • Article
    Citation - WoS: 31
    Citation - Scopus: 40
    New Solutions of the Fractional Differential Equations With Modified Mittag-Leffler Kernel
    (Asme, 2023) Baleanu, Dumitru; Odibat, Zaid
    This paper is concerned with some features of the modified Caputo-type Mittag-Leffler fractional derivative operator and its associated fractional integral operator. Mainly, new types of solutions for fractional differential equations with Mittag-Leffler kernel are generated based on a numerical algorithm developed in this paper. The suggested algorithm is used to describe the solution behavior of models involving modified Caputo-type Mittag-Leffler fractional derivatives. The results described in this paper are expected to be effectively employed in the area of simulating related fractional models.
  • Article
    Citation - WoS: 9
    Citation - Scopus: 11
    Research on a Collocation Approach and Three Metaheuristic Techniques Based on Mvo, Mfo, and Woa for Optimal Control of Fractional Differential Equation
    (Sage Publications Ltd, 2023) Khanduzi, Raheleh; Beik, Samaneh P. A.; Baleanu, Dumitru; Ebrahimzadeh, Asiyeh; A Beik, Samaneh P
    Exploiting a comprehensive mathematical model for a class of systems governed by fractional optimal control problems is the significant focal point of the current paper. The efficiency index is a function of both control and state variables and the dynamic control system relies on Caputo fractional derivatives. The attributes of Bernoulli polynomials and their operational matrices of fractional Riemann-Liouville integrations are applied to convert the optimization problem to the nonlinear programing problem. Executing multi-verse optimizer, moth-flame optimization, and whale optimization algorithm terminate to the most excellent solution of fractional optimal control problems. A study on the advantage and performance between these approaches is analyzed by some examples. Comprehensive analysis ascertains that moth-flame optimization significantly solves the example. Furthermore, the privilege and advantage of preference with its accuracy are numerically indicated. Finally, results demonstrate that the objective function value gained by moth-flame optimization in comparison with other algorithms effectively decreased.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 7
    A Novel Analytical Technique of the Fractional Bagley-Torvik Equations for Motion of a Rigid Plate in Newtonian Fluids
    (Tech Science Press, 2020) Ramadan, Mohamed A.; Baleanu, Dumitru; Moatimid, Galal M.; Taha, Mahmoud H.
    The current paper is concerned with a modified Homotopy perturbation technique. This modification allows achieving an exact solution of an initial value problem of the fractional differential equation. The approach is powerful, effective, and promising in analyzing some classes of fractional differential equations for heat conduction problems and other dynamical systems. To crystallize the new approach, some illustrated examples are introduced.
  • Article
    Citation - WoS: 48
    Citation - Scopus: 58
    Dynamical Analysis of Fractional Order Model of Immunogenic Tumors
    (Sage Publications Ltd, 2016) Baleanu, Dumitru; Huang, Jianfei; Tang, Yifa; Al Qurashi, Maysaa Mohamed; Arshad, Sadia
    In this article, we examine the fractional order model of the cytotoxic T lymphocyte response to a growing tumor cell population. We investigate the long-term behavior of tumor growth and explore the conditions of tumor elimination analytically. We establish the conditions for the tumor-free equilibrium and tumor-infection equilibrium to be asymptotically stable and provide the expression of the basic reproduction number. Existence of physical significant tumor-infection equilibrium points is investigated analytically. We show that tumor growth rate, source rate of immune cells, and death rate of immune cells play vital role in tumor dynamics and system undergoes saddle-node and transcritical bifurcation based on these parameters. Furthermore, the effect of cancer treatment is discussed by varying the values of relevant parameters. Numerical simulations are presented to illustrate the analytical results.