ON THE SOLUTION OF GENERALIZED FRACTIONAL KINETIC EQUATIONS
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Abstract
In view of the usefulness and a great importance of the kinetic equation in certain astrophysical problems the authors develop a new and further generalized form of the fractional kinetic equation involving Mittag-Leffler function and G-function. This new generalization can be used for the computation of the change of chemical composition in stars like the sun. The manifold generality of the Mittag-Leffler function and G-function is discussed in terms of the solution of the above fractional kinetic equation. Â Â Â
Saxena et al. [21, 22] derived the solutions of generalized fractional kinetic equations in terms of Mittaz-Leffler functions by the application of Laplace transform [9, 23]. The present work is extension of earlier work done by Saxena et al. [21, 22], and Chaurasia and Pandey [5].
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References:
Agarwal, R.P., A propos d’une note de M. Pierre Humbert; C.R. Acad. Sci. Paris 236 (1953): 2031-2032.
Asiru, M.A., Sumudu transform and the solution of integral equations of convolution type; International Journal of Mathematical Education in Science and Technology, 32(6) (2001): 906-910.
Belgacem, F.B.M. and Karaballi, A.A., Sumudu transform fundamental properties investigations and applications; International J. Appl. Math. Stoch. Anal., (2005): 1-23.
Belgacem, F.B.M., Karaballi, A.A. and Kalla, S.L., Analytical investigations of the Sumudu transform and applications to integral production equations; Mathematical Problems in Engineering, 3 (2003): 103-118.
Chaurasia, V.B.L. and Pandey, S.C., On the new computable solution of the generalized fractional kinetic equations involving the generalized function for the fractional calculus and related functions; Astrophys. Space Sci. 317, (2008): 213-219.
Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F.G., Tables of Integral Transforms; Vol. 1, McGraw-Hill, New York (1954).
Fox, C., Solving integral equations by L and L-1 operators; American Mathematical Society, 29(2): 299.
Gorenflo, R., Kilbas, A.A. and Rogozin, S., On the generalized Mittag-Leffler type functions; Integral Transforms and Special Functions 7, No. 3-4 (1998): 215-224.
Gupta, V.G. and Sharma, B., On the solutions of generalized fractional kinetic equations; Applied Mathematical Sciences, Vol. 5(19), (2011): 899-910.
Hartley, T.T. and Lorenzo, C.F., A solution to the fundamental linear fractional order differential equation; NASA/TP-1998-208693, (1998).
Haubold, H.J. and Mathai, A.M., The fractional kinetic equation and thermonuclear functions; Astrophys. Space Sci. 327 (2000): 53-63.
Haubold, H.J., Mathai, A.M. and Saxena, R.K., Mittag-Leffler functions and their applications; J. Appl. Math. (Article ID 298628) (2011): 1-51.
Hilfer, R., in: R. Hilfer (Ed.), Applications of Fractional Calculus in Physics; World Scientific, Singapore (2000).
Lorenzo, C.F. and Hartley, T.T., Generalized function for the fractional calculus; NASA/TP-1999-209424, (1999).
Mathai, A.M., Saxena, R.K. and Haubold, H.J., The H-function: Theory and Applications; Springer, New York (2010).
McLachlan, N.W., Modern Operational Calculus with Applications in technical Mathematics; Macmillan, London (1948).
Mittag-Leffler, G.M., Sur la representation analytique d’une branche uniforme d’une function monogene; Acta Math. 29 (1905): 101-181.
Mittag-Leffler, M.G., Sur la nouvelle fonction ; C.R. Acad. Sci. Paris No.137 (1903): 554-558.
Prabhakar, T.R., A singular integral equation with a generalized Mittag-Leffler function in the Kernel; Yokohama Math. J. No. 19 (1971): 7-15.
Saxena, R.K., Certain properties of generalized Mittag-Leffler function; Conference of the Society of Special functions and their Applications, Proc. 3rd annual conf., Chennai, India (2002): 78-81.
Saxena, R.K., Mathai, A.M. and Haubold, H.J., On Fractional kinetic equations; Astrophys. Space Sci. 282 (2002): 281-287.
Saxena, R.K., Mathai, A.M. and Haubold, H.J., On generalized fractional kinetic equations; Physica A 344 (2004): 657-664.
Spiegel, M.R., Theory and Problems of Laplace Transforms; Schaums Outline Series, McGraw-Hill, New York (1965).
Srivastava, H.M. and Saxena, R.K., Operators of fractional integration and their applications; Appl. Math. Comput. 118 (2001): 1-52.
Watugala, G.K., Sumudu transform- a new integral transform to solve differential equations and control engineering problems; Math. Engrg. Indust. No. 4 (6) (1998): 319-329.
Wiman, A., Uber de fundamental satz in der theorie der funktionen ; Acta Math. No. 29 (1905): 191-201.