Papers by Prof. Omar Abu Arqub
The novel cubic B-spline method for fractional Painlevé and Bagley-Trovik equations in the Caputo, Caputo-Fabrizio, and conformable fractional sense
Alexandria Engineering Journal
Analytical solutions of conformable Drinfel’d–Sokolov–Wilson and Boiti Leon Pempinelli equations via sine–cosine method
Results in Physics
Fractional delay integrodifferential equations of nonsingular kernels: existence, uniqueness, and numerical solutions using Galerkin algorithm based on shifted Legendre polynomials
International Journal of Modern Physics C
This paper considers linear and nonlinear fractional delay Volterra integrodifferential equation ... more This paper considers linear and nonlinear fractional delay Volterra integrodifferential equation of order [Formula: see text] in the Atangana–Beleanu–Caputo (ABC) sense. We used continuous Laplace transform (CLT) to find equivalent Volterra integral equations that have been used together with the Arzela–Ascoli theorem and Schauder’s fixed point theorem to prove the local existence solution. Moreover, the obtained Volterra integral equations and the contraction mapping theorem have been successfully applied to construct and prove the global existence and uniqueness of the solution for the considered fractional delay integrodifferential equation (FDIDE). The Galerkin algorithm instituted within shifted Legendre polynomials (SLPs) is applied in the approximation procedure for the corresponding delay equation. Indeed, by this algorithm, we get algebraic system models and by solving this system we gained the approximated nodal solution. The reliability of the method and reduction in the ...
A novel analytical algorithm for generalized fifth-order time-fractional nonlinear evolution equations with conformable time derivative arising in shallow water waves
Alexandria Engineering Journal, 2021
Modeling and Analyzing Neural Networks Using Reproducing Kernel Hilbert Space Algorithm
Applied Mathematics & Information Sciences, 2018
In this paper, we present a new method for solving some certai n differential systems in the arti... more In this paper, we present a new method for solving some certai n differential systems in the artificial neural networks fiel d. The analytic and approximate solutions are given with serie form in the spaces W[a,b] and H[a,b]. The method used in this the is has several advantages; first, it is of global nature in terms of the solutions obtained as well as its ability to solve othe r mathematical, physical, and engineering problems; second, it is accurate , ne d less effort to achieve the results, and is developed es pecially for the nonlinear cases; third, in the proposed method, it is possib le to pick any point in the interval of integration and as well the approximate solutions will be applicable; fourth, the method does not re quire discretization of the variables, and it is not effecte d by computation round off errors and one is not faced with necessity of large c omputer memory and time. Results presented in this thesissh ow potentiality, generality, and superiority of our method as compared with t he Range Kutta method.
Fractional crossover delay differential equations of Mittag-Leffler kernel: Existence, uniqueness, and numerical solutions using the Galerkin algorithm based on shifted Legendre polynomials
Results in Physics
Solving Fuzzy Fractional IVPs of order 2β by Residual Power Series Algorithm
2019 IEEE Jordan International Joint Conference on Electrical Engineering and Information Technology (JEEIT)
In this paper, an efficient numeric-analytic algorithm has been applied based on the residual pow... more In this paper, an efficient numeric-analytic algorithm has been applied based on the residual power series approach to solve fuzzy fractional initial value problems of order $2\beta, 0\beta\leq 1$, under the strongly generalized differentiability. The present method relies basically upon the concept of the residual functions and generalized Taylor formula that constructs analytical and approximate solutions in the form of rapidly convergent series according to their parametric form. To validate the efficiency, reliability, and applicability of the proposed approach, the experimental data has been presented.
Application of Power Series Method for Solving Obstacle Problem of Fractional Order
2019 IEEE Jordan International Joint Conference on Electrical Engineering and Information Technology (JEEIT)
An effective numerical method depends on the fractional power series is applied to solving a clas... more An effective numerical method depends on the fractional power series is applied to solving a class of boundary value problems associated with obstacle, unilateral, and contact problems of fractional order $2\alpha, 0\lt \alpha\leq 1$. The fractional derivative is considered in the Caputo sense. This method constructs a convergent sequence of approximate solutions for the obstacle problem. A numerical example is given to illustrate the higher accuracy of this technique.
Analysis of Lie Symmetry, Explicit Series Solutions, and Conservation Laws for the Nonlinear Time-Fractional Phi-Four Equation in Two-Dimensional Space
International Journal of Applied and Computational Mathematics
Development of the reproducing kernel Hilbert space algorithm for numerical pointwise solution of the time-fractional nonlocal reaction-diffusion equation
Alexandria Engineering Journal
It is notable that, the nonlocal reaction-diffusion equation carries math and computational physi... more It is notable that, the nonlocal reaction-diffusion equation carries math and computational physics to the core of extremely dynamic multidisciplinary studies that emerge from a huge assortment of uses. In this investigation, a totally new methodology for building a locally numerical pointwise solution is given by the agent the reproducing kernel algorithm. This is done utilizing a couple of generalized Hilpert spaces and their corresponding Green functions. The proposed calculation algorithm is applied to certain scalar issues problems to figure the arrangement solutions with Dirichlet constraints. By applying the procedures of the Gram-Schmidt process, orthonormalizing the basis, and truncating the optimized series, the approximate solutions are drawn, tabulated, and sketched. Introduced mathematical outcomes not only show the hidden superiority of the algorithm but also show its accurate efficiency. Finally, focused notes and futures planning works are mentioned with the most-used references.
In this paper, a powerful computational algorithm is developed for the solution of classes of sin... more In this paper, a powerful computational algorithm is developed for the solution of classes of singular second-order, three-point Volterra integrodifferential equations in favorable reproducing kernel<br>Hilbert spaces. The solutions is represented in the form of series in the Hilbert space W23 0 1 <br>with easily computable components. In finding the computational solutions, we use generating the<br>orthogonal basis from the obtained kernel functions such that the orthonormal basis is constructing in order to formulate and utilize the solutions. Numerical experiments are carried where two<br>smooth reproducing kernel functions are used throughout the evolution of the algorithm to obtain<br>the required nodal values of the unknown variables. Error estimates are proven that it converge to<br>zero in the sense of the space norm. Several computational simulation experiments are given to<br>show the good performance of the proposed procedure. Fin...
The Laplace Optimized Decomposition Method for Solving Systems of Partial Differential Equations of Fractional Order
International Journal of Applied and Computational Mathematics, 2022
arXiv: Numerical Analysis, 2017
The aim of this study is to present a good modernistic strategy for solving some well-known class... more The aim of this study is to present a good modernistic strategy for solving some well-known classes of Lane-Emden type singular differential equations. The proposed approach is based on the reproducing kernel Hilbert space (RKHS) and introducing the reproducing kernel properties in which the initial conditions of the problem are satisfied. The analytical solution that obtained involves in the form of a convergent series with easily computable terms in its reproducing kernel space. The approximation solution is expressed by n-term summation of reproducing kernel functions and it is converge to the analytical solution. Our investigations indicate that there is excellent agreement between the numerical results and the RKHS method, which is applied to some examples to illustrate the accuracy, efficiency, and applicability of the method. The present work shows the potential of the RKHS technique in solving such nonlinear singular initial value problems.
In this paper, a powerful computational algorithm is developed for the solution of classes of sin... more In this paper, a powerful computational algorithm is developed for the solution of classes of singular second-order, three-point Volterra integrodi erential equations in favorable reproducing kernel Hilbert spaces. The solutions is represented in the form of series in the Hilbert space W 3 2 [0; 1] with easily computable components. In nding the computational solutions, we use generating the orthogonal basis from the obtained kernel functions such that the orthonormal basis is constructing in order to formulate and utilize the solutions. Numerical experiments are carried where two smooth reproducing kernel functions are used throughout the evolution of the algorithm to obtain the required nodal values of the unknown variables. Error estimates are proven that it converge to zero in the sense of the space norm. Several computational simulation experiments are given to show the good performance of the proposed procedure. Finally, the utilized results show that the present algorithm and...
A numerical method for solving conformable fractional integrodifferential systems of second-order, two-points periodic boundary conditions
Alexandria Engineering Journal, 2021
Physica Scripta, 2020
Fractional exponential that are invariant under fractional derivatives, elementary and special fr... more Fractional exponential that are invariant under fractional derivatives, elementary and special fractional functions are introduced. Approximate solutions to fractional Burgers equation, by using the homotopy perturbation method, are obtained. Furthermore, real integral representations for some H-functions are found that may be very helpful in numerical computations.
Numerical Solutions of Riesz Fractional Diffusion and Advection-Dispersion Equations in Porous Media Using Iterative Reproducing Kernel Algorithm
Journal of Porous Media, 2020
Numerical computations of coupled fractional resonant Schrödinger equations arising in quantum mechanics under conformable fractional derivative sense
Physica Scripta, 2020
SSRN Electronic Journal, 2018
In this paper, we provide approximate solution to linear time-fractional Kline-Gordon equations (... more In this paper, we provide approximate solution to linear time-fractional Kline-Gordon equations (FKGEs) with initial conditions by using the residual power series (RPS) method. The proposed technique relies on generalized Taylor formula under Caputo sense aiming at extracting a supportive analytical solution in convergent series form. Graphical results show the geometric behaviors to the approximate solutions at different values of fraction order. The numerical analysis detects that the RPS technique is an efficient, simple and powerful tool to determine the solutions of the time-fractional KGE.
Alexandria Engineering Journal, 2020
This paper deals with the stability convergence analysis for SFCE in the sense of Riemann-Liouvil... more This paper deals with the stability convergence analysis for SFCE in the sense of Riemann-Liouville derivative. A modified FDDS is developed utilizing the fractionally-shifted Gru¨nwald formula in handling the SFCE. In this orientation, a novel operational matrix based on the implicit scheme is proposed for solving such issue. The stability features of steady states of the SFCE are investigated numerically. Several numerical applications using the well-known SFCE are tested to demonstrate the capability and feasibility of the method. The acquired results indicate that the proposed method is an appropriate tool for solving various fractional systems arises in physics and engineering.
Uploads
Papers by Prof. Omar Abu Arqub