Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 18Citation - Scopus: 19A New Generalized Kdv Equation: Its Lump-Type, Complexiton and Soliton Solutions(World Scientific Publ Co Pte Ltd, 2022) Hosseini, K.; Salahshour, S.; Baleanu, D.; Mirzazadeh, M.; Dehingia, K.A new generalized KdV equation, describing the motions of long waves in shallow water under the gravity field, is considered in this paper. By adopting a series of well-organized methods, the Backlund transformation, the bilinear form and diverse wave structures of the governing model are formally extracted. The exact solutions listed in this paper are categorized as lump-type, complexiton, and soliton solutions. To exhibit the physical mechanism of the obtained solutions, several graphical illustrations are given for particular choices of the involved parameters. As a direct consequence, diverse wave structures given in this paper enrich the studies on the KdV-type equations.Article Citation - WoS: 19Citation - Scopus: 22Approximating System of Ordinary Differential-Algebraic Equations Via Derivative of Legendre Polynomials Operational Matrices(World Scientific Publ Co Pte Ltd, 2023) Abdelhakem, M.; Baleanu, D.; Agarwal, P.; Moussa, HanaaLegendre polynomials' first derivatives have been used as the basis function via the pseudo-Galerkin spectral method. Operational matrices for derivatives have been used and extended to deal with the system of ordinary differential-algebraic equations. An algorithm via those matrices has been designed. The accuracy and efficiency of the proposed algorithm had been shown by two techniques, theoretically, via the boundedness of the approximated expansion and numerically through numerical examples.Article Citation - WoS: 4Citation - Scopus: 4Double-Quasi Numerical Method for the Variable-Order Time Fractional and Riesz Space Fractional Reaction-Diffusion Equation Involving Derivatives in Caputo-Fabrizio Sense(World Scientific Publ Co Pte Ltd, 2020) Pandey, Prashant; Gomez-Aguilar, J. F.; Baleanu, D.; Kumar, SachinOur motive in this scientific contribution is to deal with nonlinear reaction-diffusion equation having both space and time variable order. The fractional derivatives which are used are non-singular having exponential kernel. These derivatives are also known as Caputo-Fabrizio derivatives. In our model, time fractional derivative is Caputo type while spatial derivative is variable-order Riesz fractional type. To approximate the variable-order time fractional derivative, we used a difference scheme based upon the Taylor series formula. While approximating the variable order spatial derivatives, we apply the quasi-wavelet-based numerical method. Here, double-quasi-wavelet numerical method is used to investigate this type of model. The discretization of boundary conditions with the help of quasi-wavelet is discussed. We have depicted the efficiency and accuracy of this method by solving the some particular cases of our model. The error tables and graphs clearly show that our method has desired accuracy.Article Citation - WoS: 19Citation - Scopus: 25Approximate Endpoint Solutions for a Class of Fractional Q-Differential Inclusions by Computational Results(World Scientific Publ Co Pte Ltd, 2020) Gomez Aguilar, J. F.; Baleanu, D.; Rezapour, Sh; Samei, M. E.; Aydogan, S. M.By using the notion of endpoints for set-valued functions and some classical fixed point techniques, we investigate the existence of solutions for two fractional q-differential inclusions under some integral boundary value conditions. By providing an example, we illustrate our main result about endpoint. Also, we give some related algorithms and numerical results.Article Citation - WoS: 28Citation - Scopus: 30A Fractal Fractional Model for Cervical Cancer Due To Human Papillomavirus Infection(World Scientific Publ Co Pte Ltd, 2021) Ahmed, N.; Raza, A.; Iqbal, Z.; Rafiq, M.; Rehman, M. A.; Baleanu, D.; Akgul, A.In this paper, we have investigated women's malignant disease, cervical cancer, by constructing the compartmental model. An extended fractal-fractional model is used to study the disease dynamics. The points of equilibria are computed analytically and verified by numerical simulations. The key role of R-0 in describing the stability of the model is presented. The sensitivity analysis of R-0 for deciding the role of certain parameters altering the disease dynamics is carried out. The numerical simulations of the proposed numerical technique are demonstrated to test the claimed facts.Article Citation - WoS: 14Citation - Scopus: 18Efficient Numerical Treatments for a Fractional Optimal Control Nonlinear Tuberculosis Model(World Scientific Publ Co Pte Ltd, 2018) AL-Mekhlafi, S. M.; Baleanu, D.; Sweilam, N. H.In this paper, the general nonlinear multi-strain Tuberculosis model is controlled using the merits of Jacobi spectral collocation method. In order to have a variety of accurate results to simulate the reality, a fractional order model of multi-strain Tuberculosis with its control is introduced, where the derivatives are adopted from Caputo's definition. The shifted Jacobi polynomials are used to approximate the optimality system. Subsequently, Newton's iterative method will be used to solve the resultant nonlinear algebraic equations. A comparative study of the values of the objective functional, between both the generalized Euler method and the proposed technique is presented. We can claim that the proposed technique reveals better results when compared to the generalized Euler method.Article Citation - WoS: 2Citation - Scopus: 7Some New Soliton-Like and Doubly Periodic-Like Solutions of Fisher Equation With Time-Dependent Coefficients(World Scientific Publ Co Pte Ltd, 2018) El-Shazly, E.; Baleanu, D.; Elsaidi, A.; Nour, H. M.; Latif, M. S. Abdel; Elsaid, A.; Abdel Latif, M.S.In this paper, the group classification is presented for Fisher equation with time-dependent coefficients. The analysis provided many new solutions that take the form of doubly periodic-like solutions and soliton-like solutions.