Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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FRACTIONAL SOLUTIONS OF A CONFLUENT HYPERGEOMETRIC EQUATION

  • Published : 2012.05.15
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Abstract

By means of fractional calculus techniques, we find explicit solutions of confluent hypergeometric equations. We use the N-fractional calculus operator $N^{\mu}$ method to derive the solutions of these equations.

Keywords

References

  1. A. Erdelyi, W. Magnus, F. Oberhettinger, F. G. Tricomi, Tables of Integral Transform, II, McGraw-Hill Book Company, New York, Toronto and London, 1954.
  2. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations,Theory and Applications of Fractional Differ- ential Equations, North-Holland Mathematical Studies 204, Elsevier (North- Holland) Science Publishers, Amsterdam, London and New York, 2006.
  3. K. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, 1993.
  4. K. Nishimoto, An Essence of Nishimoto's Fractional Calculus (Calculus of the 21 st Century): Integrations and Differentiations of Arbitrary Order, Descartes Press, Koriyama, 1991.
  5. K. Nishimoto, Fractional Calculus, I, II, III, IV, V, Descartes Press, Koriyama, 1984, 1987, 1989, 1991 and 1996.
  6. K. Nishimoto, Kummer's Twenty-Four Functions and N-Fractional Calculus, Nonlinear Analysis, Theory, Methods & Applications, 30 (2)(1997), 1271-1282. https://doi.org/10.1016/S0362-546X(96)00245-3
  7. K. Oldham, J. Spanier, The Fractional Calculus; Theory and Applications of Differentiation and Integration to Arbitrary Order (Mathematics in Science and Engineering, V), Academic Press, 1974.
  8. I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, Methods of Their Solution and Some of Their Applications, Mathematics in Science and Enginering, vol. 198, Academic Press, New York, London, Tokyo and Toronto, 1999.
  9. S. S. de Romero, H. M. Srivastava, An Application of the N- Fractional Calculus Operator method to a Modified Whittaker Equation, Appl. Math. and Comp. 115 (2000), 11-21. https://doi.org/10.1016/S0096-3003(99)00130-7
  10. B. Ross, Fractional Calculus and Its Applications, Conference Proceedings held at the University of New Haven, June 1974, Springer, New York, 1975.
  11. S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications Translated from the Russian: Integrals and Deriva- tives of Fractional Order and Some of Their Applications ("Nauka i Tekhnika", Minsk, 1987), Gordon and Breach Science Publishers, Reading, Tokyo, Paris, Berlin and Langhorne (Pennsylvania), 1993.
  12. H. M. Srivastava, S. Owa, K. Nishimoto, Some Fractional Differintegral Equa- tions, J. Math. Anal. Appl. 106 (1985), 360-366. https://doi.org/10.1016/0022-247X(85)90117-9

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