A simple fractional-calculus approach to the solutions of the Bessel differential equation of general order and some of its applications

Computers and Mathematics with Applications

Volumn 49, Issue 9-10, 2005, Pages 1487-1498

  Lin, Shy Der ^a   Ling, Wei Chich ^a   Nishimoto, Katsuyuki ^b   Srivastava, H M ^c  

^a CHUNG YUAN CHRISTIAN UNIVERSITY   (Taiwan)

^b Descartes Press Company   (Japan)

^c UNIVERSITY OF VICTORIA   (Canada)

Author keywords

Bessel differential equation; Differentegral equations; Fractional calculus; Frobenius method; Fuchsian (and non Fuchsian) equations; Generalized Leibniz rule; Index law; Linear (ordinary and partial) differential equations; Linearity property

Indexed keywords

FRACTALS; INTEGRODIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; NUMBER THEORY; PROBLEM SOLVING; QUADRATIC PROGRAMMING; TOPOLOGY;

BASSEL FUNCTIONS; BESSEL DIFFERENTIAL EQUATION; FRACTIONAL CALCULUS; TRIGONOMETRIC FUNCTIONS;

DIFFERENTIATION (CALCULUS);

EID: 23344432380     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2004.09.009     Document Type: Article

References (27)

1. R. Hilfer Applications of Fractional Calculus in Physics 2000 World Scientific Publishing Company
2. H.M. Ozaktas, Z. Zalevsky, and M.A. Kutay The Fractional Fourier Transform with Applications in Optics and Signal Processing Wiley Series in Pure and Applied Optics 2000 John Wiley and Sons Singapore
3. I. Podlubny Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications Mathematics in Science and Engineering Volume 198 1999 Academic Press New York
4. K.S. Miller, and B. Ross An Introduction to the Fractional Calculus and Fractional Differential Equations A Wiley-Interscience Publication 1993 John Wiley and Sons New York
5. S.-T. Tu, D.-K. Chyan, and H.M. Srivastava Some families of ordinary and partial fractional differintegral equations Integral Transform. Spec. Funct. 11 2001 291 302
6. C.-Y. Lee, H.M. Srivastava, and W.-C. Yueh Explicit solutions of some linear ordinary and partial fractional differintegral equations Appl. Math. Comput. 144 2003 11 25
7. S.-D. Lin, J.-C. Shyu, K. Nishimoto, and H.M. Srivastava Explicit solutions of some general families of ordinary and partial differential equations associated with the Bessel equation by means of fractional calculus J. Fract. Calc. 25 2004 33 45
8. S.-D. Lin, S.-T. Tu, I-C. Chen, and H.M. Srivastava Explicit solutions of a certain family of fractional differintegral equations Hyperion Sci. J. Ser. A Math. Phys. Electr. Engrg. 2 2001 85 90
9. S.-D. Lin, H.M. Srivastava, S.-T. Tu, and P.-Y. Wang Some families of linear ordinary and partial differential equations solvable by means of fractional calculus Internat. J. Differential Equations Appl. 4 2002 405 421
10. S.-D. Lin, S.-T. Tu, and H.M. Srivastava Explicit solutions of certain ordinary differential equations by means of fractional calculus J. Fract. Calc. 20 2001 35 43
11. S.-D. Lin, S.-T. Tu, and H.M. Srivastava Certain classes of ordinary and partial differential equations solvable by means of fractional calculus Appl. Math. Comput. 131 2002 223 233
12. S.-D. Lin, S.-T. Tu, and H.M. Srivastava Explicit solutions of some classes of non-Fuchsian differential equations by means of fractional calculus J. Fract. Calc. 21 2002 49 60
13. S.-D. Lin, S.-T. Tu, and H.M. Srivastava A unified presentation of certain families of non-Fuchsian differential equations via fractional calculus operators Computers Math. Applic. 45 12 2003 1861 1870
14. S.-D. Lin, S.-T. Tu, H.M. Srivastava, and P.-Y. Wang Certain operators of fractional calculus and their applications to differential equations Computers Math. Applic. 44 12 2002 1557 1565
15. S. Salinas de Romero, and H.M. Srivastava An application of the N-fractional calculus operator method to a modified Whittaker equation Appl. Math. Comput. 115 2000 11 21
16. S.-T. Tu, Y.-T. Huang, I-C. Chen, and H.M. Srivastava A certain family of fractional differintegral equations Taiwanese J. Math. 4 2000 417 426
17. S.-T. Tu, S.-D. Lin, Y.-T. Huang, and H.M. Srivastava Solutions of a certain class of fractional differintegral equations Appl. Math. Lett. 14 2 2001 223 229
18. S.-T. Tu, S.-D. Lin, and H.M. Srivastava Solutions of a class of ordinary and partial differential equations via fractional calculus J. Fract. Calc. 18 2000 103 110
19. II, III, IV, and V K. Nishimoto (1987), (1989), (1991), and (1996) Fractional Calculus Volume I 1984 Descartes Press New York
20. st Century: Integrations and Differentiations of Arbitrary Order 1991 Descartes Press Koriyama
21. H.M. Srivastava, S. Owa, and K. Nishimoto Some fractional differintegral equations J. Math. Anal. Appl. 106 1985 360 366
22. A. Erdélyi, W. Magnus, F. Oberhettinger, and F.G. Tricomi Higher Transcendental Functions Volume II 1953 McGraw-Hill Book Company Koriyama
23. G.N. Watson A Treatise on the Theory of Bessel Functions Second Edition 1944 Cambridge University Press New York
24. E.T. Whittaker, and G.N. Watson A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; With an Account of the Principal Transcendental Functions Fourth Edition 1927 Cambridge University Press Cambridge
25. Reprinted by Dover Publications, New York, (1956) E.L. Ince Ordinary Differential Equations 1927 Longmans, Green and Company Cambridge
26. K. Nishimoto Applications of N-transformation and N-fractional calculus method to nonhomogeneous Bessel equations (I) J. Fract. Calc. 8 1995 25 30
27. Rome F.G. Tricomi Funzioni Ipergeometriche Confluenti Edizioni Cremonese 1954