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© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.

Abstract

In this paper, an approximate method combining the finite difference and collocation methods is studied to solve the generalized fractional diffusion equation (GFDE). The convergence and stability analysis of the presented method are also established in detail. To ensure the effectiveness and the accuracy of the proposed method, test examples with different scale and weight functions are considered, and the obtained numerical results are compared with the existing methods in the literature. It is observed that the proposed approach works very well with the generalized fractional derivatives (GFDs), as the presence of scale and weight functions in a generalized fractional derivative (GFD) cause difficulty for its discretization and further analysis.

Details

Title
Finite Difference–Collocation Method for the Generalized Fractional Diffusion Equation
Author
Kumar, Sandeep 1   VIAFID ORCID Logo  ; Pandey, Rajesh K 1   VIAFID ORCID Logo  ; Kumar, Kamlesh 2   VIAFID ORCID Logo  ; Kamal, Shyam 3 ; Dinh, Thach Ngoc 4   VIAFID ORCID Logo 

 Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Varanasi 221005, Uttar Pradesh, India; [email protected] 
 Department of Mathematics, Manav Rachana University, Faridabad 121004, Haryana, India; [email protected] 
 Department of Electrical Engineering, Indian Institute of Technology (BHU) Varanasi, Varanasi 221005, Uttar Pradesh, India; [email protected] 
 Conservatoire National des Arts et Métiers (CNAM), Cedric-Laetitia, 292 Rue St-Martin, CEDEX 03, 75141 Paris, France 
First page
387
Publication year
2022
Publication date
2022
Publisher
MDPI AG
e-ISSN
25043110
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
2694000064
Copyright
© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.