Class of integrals and applications of fractional kinetic equation with the generalized multi-index Bessel function

Abstract

In this article, we have investigated certain definite integrals and various integral transforms of the generalized multi-index Bessel function, such as Euler transform, Laplace transform, Whittaker transform, K-transform and Fourier transforms. Also found the applications of the problem on fractional kinetic equation pertaining to the generalized multi-index Bessel function using the Sumudu transform technique. Mittage-Leffler function is used to express the results of the solutions of fractional kinetic equation as well as its special cases. The results obtained are significance in applied problems of science, engineering and technology.

Fractional q-Calculus Operators Pertaining to the q-Analogue of M-Function and Its Application to Fractional q-Kinetic Equations

“…If we set r = s = 1, c 1 = δ, d 1 = 1 in Theorem 5 and by using definition (17), we have the following outcomes, that is, a q-analogue of the results obtained by Garg and Chanchlani [[27], p.39, eq. 30].…”

“…In 2000, Haubold and Mathai [10] developed a fractional differential equation involving the reaction's rate of change, the destruction rates, and the production rate. We discovered several papers in the literature that investigate extensions and generalizations of these equations utilizing different fractional calculus operators, for example, the work of Saxena et al [11][12][13], Kumar et al [14,15], Suthar et al [16,17], Habenom et al [18], Baleanu et al [19], and Gupta and Parihar [20].…”

Solutions of Fractional Kinetic Equations using the $(p,q;l)$-Extended τ -Gauss Hypergeometric Function

“…Readers can refer to [13][14][15][16][17][18][19][20] for more generalizations and extensions of extended fractional kinetic equations.…”

Application of the Laplace Transform to a New Form of Fractional Kinetic Equation Involving the Composition of the Galúe Struve Function and the Mittag–Leffler Function

“…ereafter, a frequent study of these equations was carried out by several researchers to explore the new applications. Saxena et al [3], Gupta and Parihar [4], Gupta et al [5], Habenom et al [6,7], Suthar et al [8][9][10][11], Nisar et al [12], Saichev and Zaslavsky [13], Zaslavsky [14], Agarwal and Bhargava [15], and Agrawal et al [16], Prasad Sharma and Bhargava [17], and Jain and Bhargava [18], Din [19], Din et. al.…”