Article ID: MTJPAM-D-19-00010

Title: ON CERTAIN SOLUTIONS OF A GENERALIZED PERL’S VECTOR EQUATION INVOLVING FRACTIONAL TIME DERIVATIVE


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-19-00010; Volume 1 / Issue 2 / Year 2019, Pages 42-57

Document Type: Research Paper

Author(s): Hemant Kumar a , M. A. Pathan b , Surya Kant Rai c

aDepartment of Mathematics, D. A-V. Postgraduate College Kanpur – 208001 India

bCentre for Mathematical and Statistical Sciences, Peechi Campus, Peechi – 680653, Kerala, India

cDepartment of Mathematics, D. A-V. Postgraduate College Kanpur – 208001 India

Received: 10 December 2019, Accepted: 19 December 2019, Available online: 28 December 2019.

Corresponding Author: M. A. Pathan (Email address: mapathan@gmail.com)

Full Text: PDF

Abstract

In this paper, we extricate a generalized Perl’s vector equation of heat and matter distribution in body tissue by degenerating it into an equation involving several space-dimensional Sturm-Liouville operators along with fractional time derivative. Then we evaluate some of its solutions by imposing different initial and boundary conditions. The analytical and numerical studies of this problem has revealed interesting properties, which in some sense can be regarded as an extension of the properties of the special functions like Voigt functions, Lauricella functions and Sturve functions on using certain improper integral transformations. In this connection the relevance of Voigt functions, Lauricella’s functions and Sturve functions and their multivariable extensions in mathematical physics has been emphasized.

Keywords: Generalized Perl’s vector equation, Sturm-Liouville problems, Caputo fractional derivative, special functions

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