New Generalization of Fractional Kinetic Equation using Multivariable Aleph-Function

F.Y. Ayant

doi:https://doi.org/10.14445/22315373/IJMTT-V33P511

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 33 | Number 2 | Year 2016 | Article Id. IJMTT-V33P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V33P511

New Generalization of Fractional Kinetic Equation using Multivariable Aleph-Function

F.Y. Ayant

Citation :

F.Y. Ayant, "New Generalization of Fractional Kinetic Equation using Multivariable Aleph-Function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 33, no. 2, pp. 74-83, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V33P511

Abstract

Recently A.Choudhary et al [5] use the multivariable H-function for solving generalized fractional kinetic equation. Motivated by the recent work , we present a new generalization of fractional kinetic equation by using multivariable Aleph-function. The new generalization can be used for the computation of the change of chemical composition in stars like the sun. The solution of the generalized fractional kinetic equation involving multivariable Aleph-function is obtained with help of the Laplace transform method. Further, the same generalized fractional kinetic equation is solved by using the Sumudu transform method. The solution of the proposed problem is presented in a compact form in term of the multivariable Aleph-function. Some special cases, involving the multivariable H-function, the H-function of two variables and the Aleph function of one variable are also considered.

Keywords

Multivariable Aleph-function. Fractional Kinetic equation. Laplace transform. Sumudu Transform. Riemann-Liouville fractional integral.

References

[1] F. B. M. Belgacem and A. A. Karaballi, Sumudu transform fundamental properties investigations and applications, International J. Appl. Math.Stoch. Anal., (2005), 1-23.
[2] F. B. M. Belgacem, A. A. Karaballi and S. L Kalla, Analytical investigations of the Sumudu transform and applications to integral production equations, Mathematical problems in Engineering, 3(2003), 103-118.
[3] V. B. L. Chaurasia and J. Singh, Application of Sumudu Transform in Fractional Kinetic Equations, Gen. Math. Notes, 2(1) (2011), 86-95.
[4] V. B. L. Chaurasia and J. Singh, Application of Sumudu Transform in Schrodinger Equation Occurring in Quantum Mechanics, Applied Mathematical Sciences, 4(57)(2010), 2843-2850.
[5] A.Choudhary , D.Kumar and J.Singh , New generalization of fractional kinetic equation using the multivariable H-function , Journal of Fractional Calculus and Applications , Vol 5 (3S) No,.21 ,page 1-9
[6] H. J.Haubold and A. M. Mathai, The fractional kinetic equation and thermonuclear functions, Astrophysics and Space-Sciences, 327 (2000), 53-63.
[7]D .Kumar and J.Choi, Solutions of generalized fractional kinetic equation involving Aleph-function, Mathematical Communications, Vol20(2015) , 113-123.
[8] A. M. Mathai, R. K. Saxena and H. J. Haubold, On fractional kinetic equations, Astrophys. Space Sci., 282(2002), 281-287.
[9] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, New York, (1993).
[10] K. B. Oldhman and J. Spanier, The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order, Academic Press, New York, 1974.
[11] G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, New York, (1993).
[12] C.K. Sharma and S.S. Ahmad : On the multivariable I-function. Acta ciencia Indica Math , 1992 vol 19
[13] H.M. Srivastava, K.C. Gupta and S.P. Goyal, The H -Functions of One and Two Variables, South Asian Publishers Pvt. Ltd., New Delhi, (1982).
[14] H. M. Srivastava and R. K. Saxena, Operators of fractional integration and their applications, Applied Mathematics and Computation 118, (2001), 1-52.
[15] G. K. Watugala, Sumudu transform- a new integral transform to solve differential equations and control engineering problems, Math. Engg. Indust. 6(4) (1998), 319-329