- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
The Scientific World Journal
Volume 2013 (2013), Article ID 685695, 8 pages
Fractional Solutions of Bessel Equation with -Method
Department of Mathematics, Firat University, 23119 Elazig, Turkey
Received 30 April 2013; Accepted 16 July 2013
Academic Editors: R. M. Guedes, Z. Mukandavire, and R. Wangkeeree
Copyright © 2013 Erdal Bas et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- L. Adam, Fractional Calculus: History, Definitions and Applications For the Engineer, 2004.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematical Studies, Elsevier (North-Holland) Science Publishers, Amsterdam, The Netherlands, 2006.
- 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, NY, USA, 1999.
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications Translated From the Russian: Integrals and Derivatives of Fractional Order and Some of Their Applications, “Nauka i Tekhnika”, Minsk, (1987), Gordon and Breach Science Publishers, Reading, UK, 1993.
- K. B. Oldham and J. Spanier, The Fractional Calculus, Akademic Press, New York, NY, USA, 1974.
- K. Nishimoto, Fractional Calculus, vol. I, Descartes Press, Koriyama, Japan, 1984.
- K. Nishimoto, Fractional Calculus, vol. II, Descartes Press, Koriyama, Japan, 1987.
- K. Nishimoto, Fractional Calculus, vol. III, Descartes Press, Koriyama, Japan, 1989.
- K. Nishimoto, Fractional Calculus, vol. IV, Descartes Press, Koriyama, Japan, 1991.
- K. Nishimoto, Fractional Calculus, vol. V, Descartes Press, Koriyama, Japan, 1996.
- K. Nishimoto and S. S. de Romero, “-fractional calculus operator method to nonhomogeneous and homogeneous Whittaker Equations,” Journal of Fractional Calculus, vol. 9, pp. 17–22, 1996.
- K. Nishimoto, An Essence of Nishimoto’s Fractional Calculus (Calculus of the 21st Century): Integrations and Differentiations of Arbitrary Order, Descartes Press, Koriyama, Japan, 1991.
- M. Coz and P. Rochus, “Translation kernels for velocity dependent interactions,” Journal of Mathematical Physics, vol. 18, no. 11, pp. 2232–2240, 1976.
- A. Erdely, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Tables of Integral Transform, vol. II, McGraw-Hill, New York, NY, USA, 1954.
- A. Erdely, “Axially symmetric potentials and fractional integration,” Journal of the Society for Industrial and Applied Mathematics, vol. 13, pp. 216–228, 1965.
- A. Weinstein, “Generalized axially symmetric potential theory,” Bulletin of the American Mathematical Society, vol. 59, pp. 20–38, 1953.
- B. Ross, Fractional Calculus and Its Applications, Conference Proceedings held at the University of New Haven, June 1974, Springer, New York, NY, USA, 1975.
- S. Salinas De Romero and H. M. Srivastava, “An application of the -fractional calculus operator method to a modified Whittaker equation,” Applied Mathematics and Computation, vol. 115, no. 1, pp. 11–21, 2000.
- H. M. Srivastava and R. G. Buschman, Theory and Applications of Convolution Integral Equations, vol. 79 of Kluwer Series on Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992.
- H. M. Srivastava, S. Owa, and K. Nishimoto, “Some fractional differintegral equations,” Journal of Mathematical Analysis and Applications, vol. 106, no. 2, pp. 360–366, 1985.
- H. Koyunbakan and E. S. Panakhov, “Transformation operator for singular Sturm-Liouville equations,” International Journal of Applied Mathematics, vol. 14, pp. 135–143, 2003.