Abstract
The subject of this paper is to derive the solution of generalized fractional kinetic equations. The results are obtained in a compact form containing the Mittag-Leffler function, which naturally occurs whenever one is dealing with fractional integral equations. The results derived in this paper provide an extension of a result given by Haubold and Mathai in a recent paper (Haubold and Mathai, 2000).
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Agarwal, R.P.: 1953, A propos d'une note de M. Pierre Humbert, C.R. Acad. Sci. Paris 236, 2031–2032.
Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F.G.: 1953, Higher Transcendental Functions, Vol. 1, McGraw-Hill, New York-Toronto-London.
Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F.G.: 1954, Tables of Integral Transforms, Vol. 1, McGraw-Hill, New York-Toronto-London.
Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F.G.: 1955, Higher Transcendental Functions, Vol. 3, McGraw-Hill, New York-Toronto-London.
Haubold, H.J. and Mathai, A.M.: 2000, The fractional kinetic equation and thermonuclear functions, Astrophysics and Space Science 327, 53–63.
Hilfer, R. (ed.): 2000, Applications of Fractional Calculus in Physics, World Scientific, Singapore.
Humbert, P.: 1953, Quelques resultats relatifs a'la fonction de Mittag-Leffler, C.R. Acad. Sci. Paris 236, 1467–1468.
Humbert, P. and Agarwal, R.P.: 1953, Sur la fonction de Mittag-Leffler et quelques-unes de ses generalisations, Bull. Sci. Math. (Ser.II) 77, 180–185.
Lang, K.R.: 1999, Astrophysical Formulae Vol. I (Radiation, Gas Processes and High Energy Astrophysics) and Vol. II (Space, Time, Matter and Cosmology), Springer-Verlag, Berlin-Heidelberg.
Lavagno, A. and Quarati, P.: 2002, Classical and quantum non-extensive statistics effects in nuclear many-body problems, Chaos, Solitons and Fractals 13, 569–580.
Miller, K.S. and Ross, B.: 1993, An Introduciton to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, New York.
Mittag-Leffler, G.M.: 1903, Sur la nouvelle fonction E α (x), C.R. Acad. Sci. Paris, (Ser.II) 137, 554–558.
Mittag-Leffler, G.M.: 1905, Sur la representatin analytique d'une branche uniforme d'une fonciton monogene, Acta Math. 29, 101–181.
Oldham, K.B. and Spanier, J.: 1974, The Fractional Calculus: Theory and Applications of Differentation and Integration to Arbitrary Order, Academic Press, New York.
Srivastava, H.M. and Saxena, R.K.: 2001, Operators of fractional integration and their applications, Appl. Math. Comp. 118, 1–52.
Tsallis, C.: 2002, Entropic nonextensivity: A possible measure of complexity, Chaos, Solitons and Fractals 13, 371–391.
Wiman, A.: 1905, Ueber den Fundamentalsatz in der Theorie der Funktionen E α (x), Acta Math. 29, 191–201.
Wiman, A.: 1905, Ueber die Nullstellen der Funktionen E α (x), Acta Math. 29, 217–234.
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Saxena, R., Mathai, A. & Haubold, H. On fractional kinetic equations. Astrophysics and Space Science 282, 281–287 (2002). https://doi.org/10.1023/A:1021175108964
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DOI: https://doi.org/10.1023/A:1021175108964