Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 8Citation - Scopus: 8Analytical Approximate Solutions of (n+1)-Dimensional Fractal Heat-Like and Wave-Like Equations(Mdpi, 2017) Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Sakar, Mehmet Giyas; Acan, OmerIn this paper, we propose a new type (n + 1)-dimensional reduced differential transform method (RDTM) based on a local fractional derivative (LFD) to solve (n + 1)-dimensional local fractional partial differential equations (PDEs) in Cantor sets. The presented method is named the (n + 1)-dimensional local fractional reduced differential transform method (LFRDTM). First the theories, their proofs and also some basic properties of this procedure are given. To understand the introduced method clearly, we apply it on the (n + 1)-dimensional fractal heat-like equations (HLEs) and wave-like equations (WLEs). The applications show that this new technique is efficient, simply applicable and has powerful effects in (n + 1)-dimensional local fractional problems.Article Citation - WoS: 10Citation - Scopus: 15A Novel Computational Approach To Approximate Fuzzy Interpolation Polynomials(Springer international Publishing Ag, 2016) Jafari, Raheleh; Al Qurashi, Maysaa Mohamed; Baleanu, Dumitru; Jafarian, Ahmad; Mohamed Al Qurashi, MaysaaThis paper build a structure of fuzzy neural network, which is well sufficient to gain a fuzzy interpolation polynomial of the form y(p) = a(n)x(p)(n) +... + a(1)x(p) + a(0) where a(j) is crisp number (for j = 0,..., n), which interpolates the fuzzy data (x(j), y(j)) (for j = 0,..., n). Thus, a gradient descent algorithm is constructed to train the neural network in such a way that the unknown coefficients of fuzzy polynomial are estimated by the neural network. The numeral experimentations portray that the present interpolation methodology is reliable and efficient.Article Citation - WoS: 27Citation - Scopus: 32Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations With Riesz Derivative(Mdpi, 2018) Baleanu, Dumitru; Huang, Jianfei; Al Qurashi, Maysaa Mohamed; Tang, Yifa; Zhao, Yue; Arshad, SadiaIn this article, a numerical scheme is formulated and analysed to solve the time-space fractional advection-diffusion equation, where the Riesz derivative and the Caputo derivative are considered in spatial and temporal directions, respectively. The Riesz space derivative is approximated by the second-order fractional weighted and shifted Grunwald-Letnikov formula. Based on the equivalence between the fractional differential equation and the integral equation, we have transformed the fractional differential equation into an equivalent integral equation. Then, the integral is approximated by the trapezoidal formula. Further, the stability and convergence analysis are discussed rigorously. The resulting scheme is formally proved with the second order accuracy both in space and time. Numerical experiments are also presented to verify the theoretical analysis.Article Citation - WoS: 11Citation - Scopus: 13On Solving Fractional Mobile/Immobile Equation(Sage Publications Ltd, 2017) Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Pourbashash, HosseinIn this article, a numerical efficient method for fractional mobile/immobile equation is developed. The presented numerical technique is based on the compact finite difference method. The spatial and temporal derivatives are approximated based on two difference schemes of orders O(T2-alpha) and O(h(4)), respectively. The proposed method is unconditionally stable and the convergence is analyzed within Fourier analysis. Furthermore, the solvability of the compact finite difference approach is proved. The obtained results show the ability of the compact finite difference.Article Citation - WoS: 45Citation - Scopus: 60Bateman-Feshbach Tikochinsky and Caldirola-Kanai Oscillators With New Fractional Differentiation(Mdpi, 2017) Francisco Gomez-Aguilar, Jose; Baleanu, Dumitru; Cordova-Fraga, Teodoro; Fabricio Escobar-Jimenez, Ricardo; Olivares-Peregrino, Victor H.; Al Qurashi, Maysaa Mohamed; Coronel-Escamilla, Antonio; Gómez-Aguilar, José Francisco; Escobar-Jiménez, Ricardo FabricioIn this work, the study of the fractional behavior of the Bateman-Feshbach-Tikochinsky and Caldirola-Kanai oscillators by using different fractional derivatives is presented. We obtained the Euler-Lagrange and the Hamiltonian formalisms in order to represent the dynamic models based on the Liouville-Caputo, Caputo-Fabrizio-Caputo and the new fractional derivative based on the Mittag-Leffler kernel with arbitrary order . Simulation results are presented in order to show the fractional behavior of the oscillators, and the classical behavior is recovered when is equal to 1.Article Citation - WoS: 49Citation - Scopus: 51Fractional Advection Differential Equation Within Caputo and Caputo-Fabrizio Derivatives(Sage Publications Ltd, 2016) Agheli, Bahram; Al Qurashi, Maysaa Mohamed; Baleanu, DumitruIn this research, we applied the variational homotopic perturbation method and q-homotopic analysis method to find a solution of the advection partial differential equation featuring time-fractional Caputo derivative and time-fractional Caputo-Fabrizio derivative. A detailed comparison of the obtained results was reported. All computations were done using Mathematica.Article Citation - WoS: 48Citation - Scopus: 58Dynamical Analysis of Fractional Order Model of Immunogenic Tumors(Sage Publications Ltd, 2016) Baleanu, Dumitru; Huang, Jianfei; Tang, Yifa; Al Qurashi, Maysaa Mohamed; Arshad, SadiaIn 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.Article Citation - WoS: 75Citation - Scopus: 110Analytical Solutions of the Electrical Rlc Circuit Via Liouville-Caputo Operators With Local and Non-Local Kernels(Mdpi, 2016) Fabian Morales-Delgado, Victor; Antonio Taneco-Hernandez, Marco; Baleanu, Dumitru; Fabricio Escobar-Jimenez, Ricardo; Mohamed Al Qurashi, Maysaa; Francisco Gomez-Aguilar, Jose; Taneco-Hernández, Marco Antonio; Al Qurashi, Maysaa Mohamed; Morales-Delgado, Victor Fabian; Gómez-Aguilar, José Francisco; Escobar-Jiménez, Ricardo FabricioIn this work we obtain analytical solutions for the electrical RLC circuit model defined with Liouville-Caputo, Caputo-Fabrizio and the new fractional derivative based in the Mittag-Leffler function. Numerical simulations of alternative models are presented for evaluating the effectiveness of these representations. Different source terms are considered in the fractional differential equations. The classical behaviors are recovered when the fractional order a is equal to 1.