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Fractal Fract
Volume 6
Issue 9
10.3390/fractalfract6090492
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Article

Solving Two-Sided Fractional Super-Diffusive Partial Differential Equations with Variable Coefficients in a Class of New Reproducing Kernel Spaces

by
Zhiyuan Li
,
Qintong Chen
,
Yulan Wang
* and
Xiaoyu Li
College of Science, Inner Mongolia University of Technology, Hohhot 010051, China
*
Author to whom correspondence should be addressed.
Fractal Fract. 2022, 6(9), 492; https://doi.org/10.3390/fractalfract6090492
Submission received: 25 July 2022 / Revised: 18 August 2022 / Accepted: 30 August 2022 / Published: 1 September 2022
(This article belongs to the Special Issue Fractional Diffusion Equations: Numerical Analysis, Modeling and Application)
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Abstract

Fractional-order calculus has become a useful mathematical framework to describe the complex super-diffusive process; however, numerical solutions of the two-sided space-fractional super-diffusive model with variable coefficients are difficult to obtain, and almost no method can obtain an analytical solution. In this paper, a class of new fractional dimensional reproducing kernel spaces (RKS) based on Caputo fractional derivatives is given, and we give analytical and numerical solutions of the two-sided space-fractional super-diffusive model based on the class of new RKS. The analytical solution is represented in the form of series in the reproducing kernel space. Numerical experiments indicate that the piecewise reproducing kernel method is more accurate than the traditional reproducing kernel method (RKM), and these new fractional reproducing kernel spaces are efficient for the two-sided space-fractional super-diffusive model.
Keywords: two-sided fractional super-diffusive model; variable coefficient; reproducing kernel space; analytical and numerical solution; reproducing kernel method two-sided fractional super-diffusive model; variable coefficient; reproducing kernel space; analytical and numerical solution; reproducing kernel method

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MDPI and ACS Style

Li, Z.; Chen, Q.; Wang, Y.; Li, X. Solving Two-Sided Fractional Super-Diffusive Partial Differential Equations with Variable Coefficients in a Class of New Reproducing Kernel Spaces. Fractal Fract. 2022, 6, 492. https://doi.org/10.3390/fractalfract6090492

AMA Style

Li Z, Chen Q, Wang Y, Li X. Solving Two-Sided Fractional Super-Diffusive Partial Differential Equations with Variable Coefficients in a Class of New Reproducing Kernel Spaces. Fractal and Fractional. 2022; 6(9):492. https://doi.org/10.3390/fractalfract6090492

Chicago/Turabian Style

Li, Zhiyuan, Qintong Chen, Yulan Wang, and Xiaoyu Li. 2022. "Solving Two-Sided Fractional Super-Diffusive Partial Differential Equations with Variable Coefficients in a Class of New Reproducing Kernel Spaces" Fractal and Fractional 6, no. 9: 492. https://doi.org/10.3390/fractalfract6090492

APA Style

Li, Z., Chen, Q., Wang, Y., & Li, X. (2022). Solving Two-Sided Fractional Super-Diffusive Partial Differential Equations with Variable Coefficients in a Class of New Reproducing Kernel Spaces. Fractal and Fractional, 6(9), 492. https://doi.org/10.3390/fractalfract6090492

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