Browsing by Author "Al Qurashi, Maysaa Mohamed"

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Citation Count: Baleanu, D...et al. (2018). A Chebyshev spectral method based on operational matrix for fractional differential equations involving non-singular Mittag-Leffler kernel, Advances in Difference Equations.
A Chebyshev spectral method based on operational matrix for fractional differential equations involving non-singular Mittag-Leffler kernel
(Pushpa Publishing House, 2018) Baleanu, Dumitru; Shiri, B.; Srivastava, H. M.; Al Qurashi, Maysaa Mohamed; 56389
In this paper, we solve a system of fractional differential equations within a fractional derivative involving the Mittag-Leffler kernel by using the spectral methods. We apply the Chebyshev polynomials as a base and obtain the necessary operational matrix of fractional integral using the Clenshaw-Curtis formula. By applying the operational matrix, we obtain a system of linear algebraic equations. The approximate solution is computed by solving this system. The regularity of the solution investigated and a convergence analysis is provided. Numerical examples are provided to show the effectiveness and efficiency of the method.
Citation Count: Baleanu, D...et al. (2017). A method for solving nonlinear Volterra's population growth model of noninteger order. ADVANCES IN DIFFERENCE EQUATIONS Published: NOV 25 2017
A method for solving nonlinear Volterra's population growth model of noninteger order
(Sprınger International Publishing, 2017) Baleanu, Dumitru; Agheli, Bahram; Firozja, M. Adabitabar; Al Qurashi, Maysaa Mohamed; 56389
Many numerical methods have been developed for nonlinear fractional integro-differential Volterra's population model (FVPG). In these methods, to approximate a function on a particular interval, only a restricted number of points have been employed. In this research, we show that it is possible to use the fuzzy transform method (F-transform) to tackle with FVPG. It makes the F-transform preferable to other methods since it can make full use of all points on this interval. We also make a comparison showing that this method is less computational and is more convenient to be utilized for coping with nonlinear integro-differential equation (IDEs), fractional nonlinear integro-differential equation (FIDEs), and fractional ordinary differential equations (FODEs).
Citation Count: Singh, Jagdev...et al. (2017). A new fractional model for giving up smoking dynamics, Advances in Difference Equations.
A new fractional model for giving up smoking dynamics
(Springer Open, 2017) Singh, Jagdev; Kumar, Devendra; Al Qurashi, Maysaa Mohamed; Baleanu, Dumitru; 56389
The key purpose of the present work is to examine a fractional giving up smoking model pertaining to a new fractional derivative with non-singular kernel. The numerical simulations are conducted with the aid of an iterative technique. The existence of the solution is discussed by employing the fixed point postulate, and the uniqueness of the solution is also proved. The effect of various parameters is shown graphically. The numerical results for the smoking model associated with the new fractional derivative are compared with numerical results for a smoking model pertaining to the standard derivative and Caputo fractional derivative.
Citation Count: Kumar, Devendra...et al. (2019). "A new fractional SIRS-SI malaria disease model with application of vaccines, antimalarial drugs, and spraying", Advances in Difference Equations.
A new fractional SIRS-SI malaria disease model with application of vaccines, antimalarial drugs, and spraying
(Springer Open, 2019) Kumar, Devendra; Singh, Jagdev; Al Qurashi, Maysaa Mohamed; Baleanu, Dumitru; 56389
The present paper deals with a new fractional SIRS-SI model describing the transmission of malaria disease. The SIRS-SI malaria model is modified by using the Caputo-Fabrizio fractional operator for the inclusion of memory. We also suggest the utilization of vaccines, antimalarial medicines, and spraying for the treatment and control of the malaria disease. The theory of fixed point is utilized to examine the existence of the solution of a fractional SIRS-SI model describing spreading of malaria. The uniqueness of the solution of SIRS-SI model for malaria is also analyzed. It is shown that the treatments have great impact on the dynamical system of human and mosquito populations. The numerical simulation of fractional SIRS-SI malaria model is performed with the aid of HATM and Maple packages to show the effect of different parameters of the treatment of malaria disease. The numerical results for fractional SIRS-SI malaria model reveal that the recommended approach is very accurate and effective.
Citation Count: İnç, M...et al. (2016). A new method for approximate solutions of some nonlinear equations: Residual power series method. Advance In Mechanical Engineering, 8(4). http://dx.doi.org/10.1177/1687814016644580
A new method for approximate solutions of some nonlinear equations: Residual power series method
(Sage Publications LTD, 2016) İnç, Mustafa; Körpınar, Zeliha S.; Al Qurashi, Maysaa Mohamed; Baleanu, Dumitru
In this work, a powerful iterative method called residual power series method is introduced to obtain approximate solutions of nonlinear time-dependent generalized Fitzhugh-Nagumo equation with time-dependent coefficients and Sharma-Tasso-Olver equation subjected to certain initial conditions. The consequences show that this method is efficient and convenient, and can be applied to a large sort of problems. The approximate solutions are compared with the known exact solutions.
Citation Count: Jafarian, Ahmad...et al. (2016). "A novel computational approach to approximate fuzzy interpolation polynomials", Springerplus, Vol. 5.
A novel computational approach to approximate fuzzy interpolation polynomials
(Springer International Publishing AG, 2016) Jafarian, Ahmad; Jafari, Raheleh; Al Qurashi, Maysaa Mohamed; Baleanu, Dumitru; 56389
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 Count: Ziane, Djelloul...et al. (2019). "An Efficient Algorithm for Solving Nonlinear Systems of Partial Differential Equations with Local Fractional Operators", Punjab Unıversity Journal of Mathematics, Vol. 51, No. 9, pp. 85-99.
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
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.
Citation Count: Singh, Jagdev...et al. (2017). Analysis of a New Fractional Model for Damped Bergers' Equation, Open Physics, 15(1), 35-41.
Analysis of a New Fractional Model for Damped Bergers' Equation
(De Gruyter Open LTD, 2017) Singh, Jagdev; Kumar, Devendra; Al Qurashi, Maysaa Mohamed; Baleanu, Dumitru; 56389
In this article, we present a fractional model of the damped Bergers' equation associated with the Caputo-Fabrizio fractional derivative. The numerical solution is derived by using the concept of an iterative method. The stability of the applied method is proved by employing the postulate of fixed point. To demonstrate the effectiveness of the used fractional derivative and the iterative method, numerical results are given for distinct values of the order of the fractional derivative.
Citation Count: Kumar, Devendra...et al. (2017). Analysis of logistic equation pertaining to a new fractional derivative with non-singular kernel, Advances in Mechanical Engineering, 9(2).
Analysis of logistic equation pertaining to a new fractional derivative with non-singular kernel
(Sage Publications LTD, 2017) Kumar, Devendra; Singh, Jagdev; Al Qurashi, Maysaa Mohamed; Baleanu, Dumitru; 56389
In this work, we aim to analyze the logistic equation with a new derivative of fractional order termed in Caputo-Fabrizio sense. The logistic equation describes the population growth of species. The existence of the solution is shown with the help of the fixed-point theory. A deep analysis of the existence and uniqueness of the solution is discussed. The numerical simulation is conducted with the help of the iterative technique. Some numerical simulations are also given graphically to observe the effects of the fractional order derivative on the growth of population.
Citation Count: Acan, O...et al. (2017). "Analytical Approximate Solutions of (N + 1)-Dimensional Fractal Heat-Like and Wave-Like Equations",Entropy, Vol. 19. No. 7.
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
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 Count: Açan, Ömer...et al. (2017). "Analytical Approximate Solutions of (n+1)-Dimensional Fractal Heat-Like and Wave-Like Equations", Entropy, Vol. 19, No. 7.
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
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 Count: Acan, Omer...et al. (2017). "Analytical Approximate Solutions of (n+1)-Dimensional Fractal Heat-Like and Wave-Like Equations", Entropy, Vol. 19, No. 7.
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
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 Count: Acan, Omer...et al. (2017) Analytical Approximate Solutions of (n+1)-Dimensional Fractal Heat-Like and Wave-Like Equations, Entropy, 19(7).
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
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 Count: Baleanu, Dumitru; Jassim, Hassan Kamil; Al Qurashi, Maysaa, "Approximate analytical solutions of Goursat problem within local fractional operators", Journal of Nonlinear Sciences and Applications, Vol. 9, No. 6, pp. 4829-4837, (2016).
Approximate analytical solutions of Goursat problem within local fractional operators
(Int Scientific Research Publications, 2016) Baleanu, Dumitru; Jassim, Hassan Kamil; Al Qurashi, Maysaa Mohamed; 56389
The local fractional differential transform method (LFDTM) and local fractional decomposition method (LFDM) are applied to implement the homogeneous and nonhomogeneous Goursat problem involving local fractional derivative operators. The approximate analytical solution of this problem is calculated in form of a series with easily computable components. Examples are studied in order to show the accuracy and reliability of presented methods. We demonstrate that the two approaches are very effective and convenient for finding the analytical solutions of partial differential equations with local fractional derivative operators. (C) 2016 All rights reserved.
Citation Count: Coronel-Escamilla, Antonio...et al. (2017). Bateman-Feshbach Tikochinsky and Caldirola-Kanai Oscillators with New Fractional Differentiation, Entropy, 19(2).
Bateman-Feshbach Tikochinsky and Caldirola-Kanai Oscillators with New Fractional Differentiation
(MDPI, 2017) Coronel-Escamilla, Antonio; Francisco Gomez-Aguilar, Jose; Baleanu, Dumitru; Cordova Fraga, Teodoro; Fabricio Escobar-Jimenez, Ricardo; Olivares-Peregrino, Victor H.; Al Qurashi, Maysaa Mohamed; 56389
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 Count: Arshad, S...et al. (2016). Dynamical analysis of fractional order model of immunogenic tumors. Advance In Mechanical Engineering, 8(7). http://dx.doi.org/10.1177/1687814016656704
Dynamical analysis of fractional order model of immunogenic tumors
(Sage Publications Ltd, 2016) Arshad, Sadia; Baleanu, Dumitru; Huang, Jianfei; Tang, Yifa; Al Qurashi, Maysaa Mohamed
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 Count: Arshad, Sadia...et al. (2018). Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations with Riesz Derivative, Entropy, 20(5).
Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations with Riesz Derivative
(MDPI, 2018) Arshad, Sadia; Baleanu, Dumitru; Huang, Jianfei; Al Qurashi, Maysaa Mohamed; Tang, Yifa; Zhao, Yue; 56389
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 Count: Baleanu, D., Agheli, B., Al Qurashi, M.M. (2016). Fractional advection differential equation within Caputo and Caputo-Fabrizio derivatives. Advances In Mechanical Engineering, 8(12). http://dx.doi.org/10.1177/1687814016683305
Fractional advection differential equation within Caputo and Caputo-Fabrizio derivatives
(Sage Publications Ltd, 2016) Baleanu, Dumitru; Agheli, Bahram; Al Qurashi, Maysaa Mohamed
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 Count: Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Al Qurashi, Maysaa' Mohamed, "Fractional calculus and application of generalized Struve function", Springerplus, Vol. 5, (2016).
Fractional calculus and application of generalized Struve function
(Springer International Publishing AG, 2016) Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; 56389
A new generalization of Struve function called generalized Galue type Struve function (GTSF) is defined and the integral operators involving Appell's functions, or Horn's function in the kernel is applied on it. The obtained results are expressed in terms of the Fox-Wright function. As an application of newly defined generalized GTSF, we aim at presenting solutions of certain general families of fractional kinetic equations associated with the Galue type generalization of Struve function. The generality of the GTSF will help to find several familiar and novel fractional kinetic equations. The obtained results are general in nature and it is useful to investigate many problems in applied mathematical science.
Citation Count: Nisar, K. S...et al. (2016). "Generalized k-Mittag-Leffler function and its composition with pathway integral operators" Journal of Nonlinear Sciences and Applications, Vol. 9, No. 6, pp. 3519-3526.
Generalized k-Mittag-Leffler function and its composition with pathway integral operators
(Int Scientific Research Publications, 2016) Nisar, Kottakkaran Sooppy; Purohit, S. D.; Abouzaid, M. S.; Al Qurashi, Maysaa Mohamed; Baleanu, Dumitru; 56389
Our purpose in this paper is to consider a more generalized form of the Mittag-Leffler function. For this newly defined function, we obtain certain composition formulas with pathway fractional integral operators. We also point out some important special cases of the main results. (C) 2016 All rights reserved.