Browsing by Author "Saad, Khaled M."

Now showing 1 - 7 of 7

Citation Count: Khader, Mohamed M...et al. (2020). "A spectral collocation method for fractional chemical clock reactions", Computational & Applied Mathematics, Vol. 39, No. 4.
A spectral collocation method for fractional chemical clock reactions
(2020) Khader, Mohamed M.; Saad, Khaled M.; Baleanu, Dumitru; Kumar, Sunil; 56389
We implement an efficient computational scheme to study the effect of precursor consumption on chemical clock reactions. The proposed model is formulated as a system of FDEs with power kernel. This paper considers the fractional derivatives of Liouville-Caputo (LC). We use the spectral collocation method (SCM) with the help of the third-kind Chebyshev polynomials. This scheme generates the fast convergent series solutions with conveniently determinable coefficients. We compute the residual error function (REF) to satisfy the accuracy of the introduced technique. This approach is an easy and efficient tool for implementing the study of such these models. We introduce a comparison between the obtained approximate solutions and those which occurred using a previously published method and excellent agreement is reported.
Citation Count: Khader, M. M...et al. (2021). "A spectral collocation method for solving fractional KdV and KdV-Burgers equations with non-singular kernel derivatives", Applied Numerical Mathematics, Vol. 161, pp. 137-146.
A spectral collocation method for solving fractional KdV and KdV-Burgers equations with non-singular kernel derivatives
(2021) Khader, M. M.; Saad, Khaled M.; Hammouch, Zakia; Baleanu, Dumitru; 56389
The purpose of this paper is to investigate the spectral collocation method with help of Chebyshev polynomials. We consider the space fractional Korteweg-de Vries and the space fractional Korteweg-de Vries-Burgers equations based on the Caputo-Fabrizio fractional derivative. The proposed method reduces the models under study to a set of ordinary differential equations and then solves the system via the finite difference method. To the best our knowledge this is the first work which studies the Caputo-Fabrizio space fractional derivative for the proposed equations. The results were validated in the case of the classic differential equations in comparison with the exact solution and the calculation of the absolute error, and in the case of fractional differential equations, the results were verified by calculating the residual error function. In both cases, the results are very accurate and effective. The presented method is easy and accurate, and can be applied to many fractional systems. (c) 2020 IMACS. Published by Elsevier B.V. All rights reserved.
Citation Count: Saad, Khaled M.; Baleanu, Dumitru; Atangana, Abdon, "New fractional derivatives applied to the Korteweg-de Vries and Korteweg-de Vries-Burger's equations", Computational & Applied Mathematics. Vol. 37, No 4, pp. 5203,5216, (2018)
New Fractional Derivatives Applied to the Korteweg-De Vries and Korteweg-De Vries-Burger's Equations
(Springer Heidelberg, 2018) Saad, Khaled M.; Baleanu, Dumitru; Atangana, Abdon; 56389
In this paper, we extend the model of the Korteweg-de Vries (KDV) and Korteweg-de Vries-Burger's (KDVB) to new model time fractional Korteweg-de Vries (TFKDV) and time fractional Korteweg-de Vries-Burger's (TFKDVB) with Liouville-Caputo (LC), Caputo-Fabrizio (CF), and Atangana-Baleanu (AB) fractional time derivative equations, respectively. We utilize the q-homotopy analysis transform method (q-HATM) to compute the approximate solutions of TFKDV and TFKDVB using LC, CF and AB in Liouville-Caputo sense. We study the convergence analysis of q-HATM by computing the Residual Error Function (REF) and finding the interval of the convergence through the h-curves. Also, we find the optimal values of h so that, we assure the convergence of the approximate solutions. The results are very effective and accurate in solving the TFKDV and TFKDVB.
Citation Count: Saad, Khaled M.; Atangana, Abdon; Baleanu, Dumitru, "New fractional derivatives with non-singular kernel applied to the Burgers equation", Chaos, Vol, 28, No. 6, (2018)
New Fractional Derivatives With Non-Singular Kernel Applied to the Burgers Equation
(Amer Inst Physics, 2018) Saad, Khaled M.; Atangana, Abdon; Baleanu, Dumitru; 56389
In this paper, we extend the model of the Burgers (B) to the new model of time fractional Burgers (TFB) based on Liouville-Caputo (LC), Caputo-Fabrizio (CF), and Mittag-Leffler (ML) fractional time derivatives, respectively. We utilize the Homotopy Analysis Transform Method (HATM) to compute the approximate solutions of TFB using LC, CF, and ML in the Liouville-Caputo sense. We study the convergence analysis of HATM by computing the interval of the convergence, the residual error function (REF), and the average residual error (ARE), respectively. The results are very effective and accurate. Published by AIP Publishing.
Citation Count: Alomari, Abedel-Karrem...et al. (2020). "Numerical solutions of fractional parabolic equations with generalized Mittag–Leffler kernels", Numerical Methods for Partial Differential Equations.
Numerical solutions of fractional parabolic equations with generalized Mittag–Leffler kernels
(2020) Alomari, Abedel-Karrem; Abdeljawad, Thabet; Baleanu, Dumitru; Saad, Khaled M.; Al-Mdallal, Qasem M.; 56389
In this article, we investigate the generalized fractional operator Caputo type (ABC) with kernels of Mittag–Lefller in three parameters Eα,µγ(λ,t) and its fractional integrals with arbitrary order for solving the time fractional parabolic nonlinear equation. The generalized definition generates infinitely many problems for a fixed fractional derivative α. We utilize this operator with homotopy analysis method for constructing the new scheme for generating successive approximations. This procedure is used successfully on two examples for finding the solutions. The effectiveness and accuracy are verified by clarifying the convergence region in the ℏ-curves as well as by calculating the residual error and the results were accurate. Based on the experiment, we verify the existence of the solution for the new parameters. Depending on these results, this treatment can be used to find approximate solutions to many fractional differential equations.
Citation Count: Saad, Khaled M.; Deniz, Sinan; Baleanu, Dumitru, "On a new modified fractional analysis of Nagumo equation", International Journal of Biomathematics, Vol. 12, No. 3, (2019).
On a new modified fractional analysis of Nagumo equation
(World Scientific Publ CO PTE LTD, 2019) Saad, Khaled M.; Deniz, Sinan; Baleanu, Dumitru; 56389
In this work, a new modified fractional form of the Nagumo equation has been presented and deeply analyzed. Using the Caputo-Fabrizio and Atangana-Baleanu time-fractional derivatives, classical Nagumo model is transformed to a new fractional version. The modified equation has been solved by using the homotopy analysis transform method. The convergence analysis has been also examined with the help of the so-called h-curves and average residual error. Comparing the obtained approximate solution with the exact solution leaves no doubt believing that the proposed technique is very efficient and converges toward the exact solution very rapidly.
Citation Count: Al Fahel, Sara;...et.al. (2023). "Quadratic and cubic logistic models involving Caputo-Fabrizio operator", European Physical Journal - Special Topics, Vol.232, No.14-15, pp.2351-2355.
Quadratic and cubic logistic models involving Caputo-Fabrizio operator
(2023) Al Fahel, Sara; Baleanu, Dumitru; Al-Mdallal, Qasem M.; Saad, Khaled M.; 56389
In this paper, we numerically investigate the fractional quadratic and cubic logistic models involving the Caputo-Fabrizio operator. We construct the successive iterations using the theory of fractional calculus and Lagrange polynomials. Then, we handled the exact solutions of these models. The validity of the accuracy and efficiency will be satisfied through some numerical results.