Remarks on 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 51, Issue 1, 2006, Pages 105-114

  Wang, Pin Yu ^a,b   Lin, Shy Der ^b   Srivastava, H M ^c  

^a Department of Mechanical Engineering Nan Ya Institute of Technology Chung Li ^*  (Taiwan)

^b CHUNG YUAN CHRISTIAN UNIVERSITY   (Taiwan)

^c UNIVERSITY OF VICTORIA   (Canada)

Author keywords

(ordinary and partial) Linear differential equations; Bessel differential equation; Bessel functions; Differintegral equations; Frobenius method; Fuchsian (and non Fuchsian) differential equations; Hypergeometric representations; Integro differential equations; Operators of fractional calculus; Polynomial coefficients; Power series solutions; Trigonometric functions

Indexed keywords

BESSEL FUNCTIONS; INTEGRODIFFERENTIAL EQUATIONS; LINEAR EQUATIONS; MATHEMATICAL OPERATORS; POLYNOMIALS; PROBLEM SOLVING; THEOREM PROVING;

(ORDINARY AND PARTIAL) LINEAR DIFFERENTIAL EQUATIONS; BESSEL DIFFERENTIAL EQUATION; DIFFERINTEGRAL EQUATIONS; FROBENIUS METHOD; FUCHSIAN (AND NON-FUCHSIAN) DIFFERENTIAL EQUATIONS; HYPERGEOMETRIC REPRESENTATIONS; OPERATORS OF FRACTIONAL CALCULUS; POWER-SERIES SOLUTIONS; TRIGONOMETRIC FUNCTIONS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 33745161562     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2005.03.021     Document Type: Article

References (34)

1. In: Hilfer R. (Ed). Applications of Fractional Calculus in Physics (2000), World Scientific Publishing Company, New York
2. Wiley Series in Pure and Applied Optics. Ozaktas H.M., Zalevsky Z., and Kutay M.A. The Fractional Fourier Transform with Applications in Optics and Signal Processing (2000), John Wiley and Sons, Singapore
3. Mathematics in Science and Engineering. Podlubny I. Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications Volume 198 (1999), Academic Press, New York
4. Miller K.S., and Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations (1993), A Wiley-Interscience Publication, John Wiley and Sons, New York
5. Tu S.-T., Chyan D.-K., and Srivastava H.M. Some families of ordinary and partial fractional differintegral equations. Integral Transform. Spec. Funct. 11 (2001) 291-302
6. Ali I., and Kalla S.L. On a class of linear integro-differential equations by fractional calculus. J. Fract. Calc. 26 (2004) 35-42
7. Lee C.-Y., Srivastava H.M., and Yueh W.-C. Explicit solutions of some linear ordinary and partial fractional differintegral equations. Appl. Math. Comput. 144 (2003) 11-25
8. Lin S.-D., Ling W.-C., Nishimoto K., and Srivastava H.M. A simple fractional-calculus approach to the solutions of the Bessel differential equation of general order and some of its applications. Computers Math. Applic. 49 9/10 (2005) 1487-1498
9. Lin S.-D., Shyu J.-C., Nishimoto K., and Srivastava H.M. 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
10. Lin S.-D., Tu S.-T., Chen I.-C., and Srivastava H.M. Explicit solutions of a certain family of fractional differintegral equations. Hyperion Sci. J. Ser. A Math. Phys. Electr. Engrg. 2 (2001) 85-90
11. Lin S.-D., Srivastava H.M., Tu S.-T., and Wang P.-Y. Some families of linear ordinary and partial differential equations solvable by means of fractional calculus. Internat. J. Differential Equations Appl. 4 (2002) 405-421
12. Lin S.-D., Tu S.-T., and Srivastava H.M. Explicit solutions of certain ordinary differential equations by means of fractional calculus. J. Fract. Calc. 20 (2001) 35-43
13. Lin S.-D., Tu S.-T., and Srivastava H.M. Certain classes of ordinary and partial differential equations solvable by means of fractional calculus. Appl. Math. Comput. 131 (2002) 223-233
14. Lin S.-D., Tu S.-T., and Srivastava H.M. Explicit solutions of some classes of non-Fuchsian differential equations by means of fractional calculus. J. Fract. Calc. 21 (2002) 49-60
15. Lin S.-D., Tu S.-T., and Srivastava H.M. A unified presentation of certain families of non-Fuchsian differential equations via fractional calculus operators. Computers Math. Applic. 45 12 (2003) 1861-1870
16. Lin S.-D., Tu S.-T., Srivastava H.M., and Wang P.-Y. Certain operations of fractional calculus and their applications to differential equations. Computers Math. Applic. 44 12 (2002) 1557-1565
17. Odibat Z., and Shawagfeh N. N-fractional calculus method to a class of linear integro-differential equations. J. Fract. Calc. 22 (2002) 83-89
18. Salinas de Romero S., and Srivastava H.M. An application of the N-fractional calculus operator method to a modified Whittaker equation. Appl. Math. Comput. 115 (2000) 11-21
19. Tu S.-T., Huang Y.-T., Chen I.-C., and Srivastava H.M. A certain family of fractional differintegral equations. Taiwanese J. Math. 4 (2000) 417-426
20. Tu S.-T., Lin S.-D., Huang Y.-T., and Srivastava H.M. Solutions of a certain class of fractional differintegral equations. Appl. Math. Lett. 14 2 (2001) 223-229
21. Tu S.-T., Lin S.-D., and Srivastava H.M. Solutions of a class of ordinary and partial differential equations via fractional calculus. J. Fract. Calc. 18 (2000) 103-110
22. Nishmoto K. Fractional Calculus Volume I (1984), Descartes Press, New York
23. Nishmoto K. Fractional Calculus Volume II (1987), Descartes Press, Koriyama
24. Nishmoto K. Fractional Calculus Volume III (1989), Descartes Press, Koriyama
25. Nishmoto K. Fractional Calculus Volume IV (1991), Descartes Press, Koriyama
26. Nishmoto K. Fractional Calculus Volume V (1996), Descartes Press, Koriyama
27. st Century): Integrations and Differentiations of Arbitrary Order (1991), Descartes Press, Koriyama
28. Srivastava H.M., Owa S., and Nishimoto K. Some fractional differintegral equations. J. Math. Anal. Appl. 106 (1985) 360-366
29. Erdélyi A., Magnus W., Oberhettinger F., and Tricomi F.G. Higher Transcendental Functions, Volume II (1953), McGraw-Hill Book Company, Koriyama
30. Watson G.N. A Treatise on the Theory of Bessel Functions. Second Edition (1944), Cambridge University Press, New York
31. Whittaker E.T., and Watson G.N. 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
32. Reprinted by Dover Publications, New York. Ince E.L. Ordinary Differential Equations (1927-1956), Longmans, Green and Company, Cambridge
33. Tricomi F.G. Funzioni Ipergeometriche Confluenti (1954), Edizioni Cremonese, London
34. Nishimoto K. Applications of N-transformation and N-fractional calculus method to nonhomogeneous Bessel equations (I). J. Fract. Calc. 8 (1995) 25-30