Journal ArticleDOI
Numerical simulation of time-fractional partial differential equations arising in fluid flows via reproducing Kernel method
TLDR
In this article, the authors presented results on the numerical simulation for classes of time-fractional PDEs such as those found in the transonic multiphase flows, which are described by the Tricomi and the Keldysh equations of Robin functions types.Abstract:
The subject of the fractional calculus theory has gained considerable popularity and importance due to their attractive applications in widespread fields of physics and engineering. The purpose of this paper is to present results on the numerical simulation for time-fractional partial differential equations arising in transonic multiphase flows, which are described by the Tricomi and the Keldysh equations of Robin functions types.,Those resulting mathematical models are solved by using the reproducing kernel method, which provide appropriate solutions in term of infinite series formula. Convergence analysis, error estimations and error bounds under some hypotheses, which provide the theoretical basis of the proposed method are also discussed.,The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the prospects of the gained results and the method are discussed through academic validations.,In this paper and for the first time: the authors presented results on the numerical simulation for classes of time-fractional PDEs such as those found in the transonic multiphase flows. The authors applied the reproducing kernel method systematically for the numerical solutions of time-fractional Tricomi and Keldysh equations subject to Robin functions types.read more
Citations
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Journal ArticleDOI
Fuzzy conformable fractional differential equations: novel extended approach and new numerical solutions
Omar Abu Arqub,Mohammed Al-Smadi +1 more
TL;DR: A new definition of fuzzy fractional derivative, so-called fuzzy conformable, is proposed and the reproducing kernel Hilbert space method in the conformable emotion is constructed side by side with numerical results, tabulated data, and graphical representations.
Journal ArticleDOI
New Illustrative Applications of Integral Transforms to Financial Models with Different Fractional Derivatives
TL;DR: The efficiency and accuracy of the Sumudu transform and decomposition series method constructed by the Laplace transform is proved in providing the solutions of several different linear/nonlinear financial models by considering the theoretical results and illustrative applications.
Journal ArticleDOI
A novel RBF-based meshless method for solving time-fractional transport equations in 2D and 3D arbitrary domains
Fractional crossover delay differential equations of Mittag-Leffler kernel: Existence, uniqueness, and numerical solutions using the Galerkin algorithm based on shifted Legendre polynomials
Journal ArticleDOI
Numerical solutions and geometric attractors of a fractional model of the cancer-immune based on the Atangana-Baleanu-Caputo derivative and the reproducing kernel scheme
TL;DR: In this paper , a mathematical model that aims to investigate the interaction between the IS and CCs by incorporating I L − 12 cytokine together with an anti-P D − L 1 inhibitor is presented.
References
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Journal ArticleDOI
Theory of Reproducing Kernels.
TL;DR: In this paper, a short historical introduction is given to indicate the different manners in which these kernels have been used by various investigators and discuss the more important trends of the application of these kernels without attempting, however, a complete bibliography of the subject matter.
Journal ArticleDOI
Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations
TL;DR: Results show that the present method and simulated annealing provide a good scheduling methodology to solve fuzzy Fredholm–Volterra integrodifferential equations.
Journal ArticleDOI
Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method
TL;DR: A new method for solving fuzzy differential equations based on the reproducing kernel theory under strongly generalized differentiability is presented, showing potentiality, generality, and superiority of the method as compared with other well-known methods.
Journal ArticleDOI
Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems
TL;DR: This paper investigates the analytic and approximate solutions of second-order, two-point fuzzy boundary value problems based on the reproducing kernel theory under the assumption of strongly generalized differentiability.
Journal ArticleDOI
Approximate analytical solution of the nonlinear fractional KdV-Burgers equation
TL;DR: The results reveal that the method is very effective and simple in determination of solution of the fractional KdV-Burgers equation.
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