High-Order Approximation to Generalized Caputo Derivatives and Generalized Fractional Advection–Diffusion Equations

Sarita Kumari, Rajesh K. Pandey () and Ravi P. Agarwal ()
Additional contact information
Sarita Kumari: Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Varanasi 221005, Uttar Pradesh, India
Rajesh K. Pandey: Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Varanasi 221005, Uttar Pradesh, India
Ravi P. Agarwal: Department of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 77553, USA

Mathematics, 2023, vol. 11, issue 5, 1-24

Abstract: In this article, a high-order time-stepping scheme based on the cubic interpolation formula is considered to approximate the generalized Caputo fractional derivative (GCFD). Convergence order for this scheme is ( 4 − α ) , where α ( 0 < α < 1 ) is the order of the GCFD. The local truncation error is also provided. Then, we adopt the developed scheme to establish a difference scheme for the solution of the generalized fractional advection–diffusion equation with Dirichlet boundary conditions. Furthermore, we discuss the stability and convergence of the difference scheme. Numerical examples are presented to examine the theoretical claims. The convergence order of the difference scheme is analyzed numerically, which is ( 4 − α ) in time and second-order in space.

Keywords: generalizedCaputo fractional derivative; generalized fractional advection–diffusion equation; difference scheme; stability; numerical solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/5/1200/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/5/1200/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:5:p:1200-:d:1084008

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().