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Discrete fractional solutions to the k ‐hypergeometric differential equation
Author(s) -
Yilmazer Resat,
Ali Karmina
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6460
Subject(s) - mathematics , fractional calculus , homogeneous differential equation , operator (biology) , differential equation , hypergeometric distribution , hypergeometric function , differential operator , mathematical analysis , homogeneous , nabla symbol , exact differential equation , algebra over a field , linear differential equation , pure mathematics , ordinary differential equation , differential algebraic equation , combinatorics , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , omega , gene
In this study, the discrete fractional nabla calculus operator is used to investigate the k ‐hypergeometric differential equation for both homogeneous and nonhomogeneous states. To solve the guiding equation, we implement certain classical transformations and also constrain the parameters needed to determine them valued. In order to achieve these results, some equipment like the Leibniz rule, the index law, the shift operator, and the power rule are set out in the frame of the discreet fractional calculus. We use all of these tools to the governing equation for homogeneous and nonhomogeneous situations. The major benefit of the fractional nabla operator is that it implements singular differential equations and converts them into fractional order equations. As a result, several new exact fractional solutions of the given equation are constructed.