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Numerical approximation of tempered fractional Sturm‐Liouville problem with application in fractional diffusion equation
Author(s) -
Yadav Swati,
Pandey Rajesh K.,
Pandey Prashant K.
Publication year - 2021
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4901
Subject(s) - mathematics , eigenfunction , eigenvalues and eigenvectors , mathematical analysis , sturm–liouville theory , fractional calculus , space (punctuation) , lebesgue integration , square integrable function , boundary value problem , physics , linguistics , philosophy , quantum mechanics
Summary In this paper, we discuss the numerical approximation to solve regular tempered fractional Sturm‐Liouville problem (TFSLP) using finite difference method. The tempered fractional differential operators considered here are of Caputo type. The numerically obtained eigenvalues are real, and the corresponding eigenfunctions are orthogonal. The obtained eigenfunctions work as basis functions of weighted Lebesgue integrable function spaceL w 2(a,b). Further, the obtained eigenvalues and corresponding eigenfunctions are used to provide weak solution of the tempered fractional diffusion equation. Approximation and error bounds of the solution of the tempered fractional diffusion equation are provided.