2020
DOI: 10.1002/fld.4901
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Numerical approximation of tempered fractional Sturm‐Liouville problem with application in fractional diffusion equation

Abstract: 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 space Lw2 (a,b). Further, the obtained eigenvalues and corresponding eigenfu… Show more

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Cited by 12 publications
(3 citation statements)
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“…In recent years, fractional calculus has been extensively used to model many phenomena of Physics, Mathematics, and several other branches of Science and Engineering. Some of the recent applications of fractional calculus are References 18‐29.…”
Section: Introductionmentioning
confidence: 99%
“…In recent years, fractional calculus has been extensively used to model many phenomena of Physics, Mathematics, and several other branches of Science and Engineering. Some of the recent applications of fractional calculus are References 18‐29.…”
Section: Introductionmentioning
confidence: 99%
“…Thus, it can describes the transition between normal and anomalous diffusions or some anomalous diffusions in finite time or bounded space domain. Many scholars have studied the tempered derivatives such as Psi-Caputo [16], Psi-Hilfer [19], Strum-Liouville [20]. In modelling, the tempered fractional calculus and the tempered fractional differential equations (TFDEs) have many real applications, such as describing rare or extreme events of stock price dynamics in finance [21] and understanding turbulence in geophysical flows [22].…”
Section: Introductionmentioning
confidence: 99%
“…In [40], Zaky studied the well-posedness of the solution aϑ(0) + be T ϑ(T) = c, and also derived and analyzed a Jacobi spectral-collocation method for the numerical solution. In [37], Yadav et. al discussed the numerical approximation to solve regular tempered fractional Sturm-Liouville problem In functional analysis the measure of noncompactness play important role which was introduced by Kuratowski [15].…”
Section: Introductionmentioning
confidence: 99%