Browsing by Author "Al Qurashi, Maysaa Mohamed"

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An Efficient Algorithm for Solving Nonlinear Systems of Partial Differential Equations with Local Fractional Operators
(Univ Punjab, 2019) Ziane, Djelloul; Cherif, Mountassir Hamdi; Baleanu, Dumitru; Belghaba, Kacem; Al Qurashi, Maysaa Mohamed; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The aim of the present study is to extend the local fractional Sumudu decomposition method (LFSDM) to resolve nonlinear systems of partial differential equations with local fractional derivatives. The derivative operators are taken in the local fractional sense. The LFSDM method provides the solution in a rapid convergent series, which may lead the non-differentiable solution in a closed form, this makes them an appropriate method for similar problems. We have provided some examples to confirm their flexibility in solving these types of systems.
Analytical Approximate Solutions of (N + 1)-Dimensional Fractal Heat-Like and Wave-Like Equations
(MDPI AG, 2017) Açan, Ömer; Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Sakar, Mehmet Giyas; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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.
Analytical Approximate Solutions of (n+1)-Dimensional Fractal Heat-Like and Wave-Like Equations
(2017) Açan, Ömer; Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Sakar, Mehmet Giyas; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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.
Citation - WoS: 7
Citation - Scopus: 7
Analytical 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, Omer; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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.
Analytical Approximate Solutions of (n+1)-Dimensional Fractal Heat-Like and Wave-Like Equations
(MDPI, 2017) Açan, Ömer; Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Sakar, Mehmet Giyas; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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.
Citation - WoS: 45
Citation - Scopus: 59
Bateman-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; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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.
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; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 27
Citation - Scopus: 30
Finite 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, Sadia; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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.
Citation - WoS: 48
Citation - Scopus: 50
Fractional Advection Differential Equation Within Caputo and Caputo-Fabrizio Derivatives
(Sage Publications Ltd, 2016) Agheli, Bahram; Al Qurashi, Maysaa Mohamed; Baleanu, Dumitru; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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.
Citation - WoS: 23
New Exact Solution of Generalized Biological Population Model
(int Scientific Research Publications, 2017) Al Qurashi, Maysaa Mohamed; Baleanu, Dumitru; Acan, Omer; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this study, a mathematical model of the generalized biological population model (GBPM) gets a new exact solution with a conformable derivative operator (CDO). The new exact solution of this model will be obtained by a new approximate analytic technique named three dimensional conformable reduced differential transform method (TCRDTM). By using this technique, it is possible to find new exact solution as well as closed analytical approximate solution of a partial differential equations (PDEs). Three numerical applications of GBPM are given to check the accuracy, effectiveness, and convergence of the TCRDTM. In these applications, obtained new exact solutions in conformable sense are compared with the exact solutions in Caputo sense in literature. The comparisons are illustrated in 3D graphics. The results show that when alpha -> 1, the exact solutions in conformable and Caputo sense converge to each other. In other cases, exact solutions different from each other are obtained. (C) 2017 All rights reserved.
Citation - WoS: 10
Citation - Scopus: 15
A Novel Computational Approach To Approximate Fuzzy Interpolation Polynomials
(Springer international Publishing Ag, 2016) Jafari, Raheleh; Al Qurashi, Maysaa Mohamed; Baleanu, Dumitru; Jafarian, Ahmad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This 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.
Citation - WoS: 9
Citation - Scopus: 12
On Solving Fractional Mobile/Immobile Equation
(Sage Publications Ltd, 2017) Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Pourbashash, Hossein; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In 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.
Citation - WoS: 23
Solutions of Nonlinear Systems by Reproducing Kernel Method
(int Scientific Research Publications, 2017) Khan, Yasir; Akgul, Esra Karatas; Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Akgul, Ali; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
A novel approximate solution is obtained for viscoelastic fluid model by reproducing kernel method (RKM). The resulting equation for viscoelastic fluid with magneto-hydrodynamic flow is transformed to the nonlinear system by introducing the dimensionless variables. Results are presented graphically to study the efficiency and accuracy of the reproducing kernel method. Results show that this method namely RKM is an efficient method for solving nonlinear system in any engineering field. (C) 2017 All rights reserved.