INTEGRAL TRANSFORM AND FRACTIONAL KINETIC EQUATION
DOI:
https://doi.org/10.22159/ijet.2022.v10i1.46890Keywords:
Fractional kinetic equation, Saigo-Maeda operator , Mittag-Leffler functionAbstract
With the help of the Laplace and Fourier transforms, we arrive at the fractional kinetic equation's solution in this paper. Their respective solutions are given in terms of the Fox's H-function and the Mittag-Leffler function, which are also known as the generalisations and the Saigo-Maeda operator-based solution of the generalised fractional kinetic equation. The paper's findings have applications in a variety of engineering, astronomy, and physical scientific fields.
References
Perdang, J, : Lecturer notes in steller stability, part I and II instito di Astronomia, Padov, (1976).
Clayton,D.D. : Principal of steller Evolution and Nucleosynthesis 2nd ed. City chicago: chicago Univ. chicago Press(1983).
Ferro, F. Lavogo.A., Quarati,P. : Temperature dependence of modified CNO nuclear reactions rates in dense stellar Plasmas (2003) arxiv:nuclth/0312106v1.
Kourganoff. V. : Introduction to the physics of steller Interiors D.Reidel Publishing company, Dordrecht(1973).
Haubold. H.J.,and Mathai, A.M., The fractional kinetic equation and thermonuclear functions, Astrophysics and space science Ap J., 327(2000) 53-63.
Mittag-Leffler function, M.G. : 1903 Sur la nouvelle function 〖 E〗_∝ (x), Comptes Rendus Acad. Sci, Paris (Ser.II) 137,554-558.
Mittag-Leffler function, M.G. : 1905 Sur la representation analytique d’une branche uniforme d’une function monogene, Acta Math.29. 101-18.
Erdelyi, A., Magnus,W., Oberhettinger, F and Tricomi, F.G. : Table of Integral Transform, McGraw-Hill, New York Vol 20, 1954.
Erdelyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F.G. : 1955, Higher Transcendental Functions, Vol.3, McGraw-Hill, New York-Toronto-London.
Dzherbashyam,M.M.:1966,Integral transform and representation of function in complex domain(in Russian),Nauka, Moscow.
Dzherbashyam,M.M.: 1993, Harmonic Analysis and Boundary Value Problems in the Complex Domain, Birkhaauser Verlag,Basel.
Prabhakar, T. R. : A singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama, Math., J., 19, 1971, 7-15.
Ahmed, H. M., On some fractional inegro-differential equations, Int. J. Contemp. Math. Science. Vol. 3, No. 2, 2008, 63-70.
Mathai,A.M and Saxena,R.K, : 1978, The H-function with application in Statistics and other disciplines,Halsted Press[John Wiley and Sons.
Srivastava, H. M. and Saigo, M. : Multiplication of fractional calculus operators and boundary value problems involving the Euler-Darboux equation, J. Math. Anal. Appl., 121, 1987, 325-369.
Published
How to Cite
Issue
Section
Copyright (c) 2023 Farooq Ahmad
This work is licensed under a Creative Commons Attribution 4.0 International License.
