A unified presentation of certain families of non-Fuchsian differential equations via fractional calculus operators

Computers and Mathematics with Applications

Volumn 45, Issue 12, 2003, Pages 1861-1870

  Lin, Shy Der ^a   Tu, Shih Tong ^a   Srivastava, H M ^b  

^a CHUNG YUAN CHRISTIAN UNIVERSITY   (Taiwan)

^b UNIVERSITY OF VICTORIA   (Canada)

Author keywords

Analytic functions; Bessel equation; Differintegral equations; Fractional calculus; Fuchsian (and non Fuchsian) differential equations; Fukuhara equation; Generalized Leibniz rule; Index law; Linearity property; Ordinary and partial differential equations; Tricomi equation; Whittaker (and modified Whittaker) equations

Indexed keywords

BESSEL FUNCTIONS; DIFFERENTIATION (CALCULUS); INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS; PROBLEM SOLVING; THEOREM PROVING;

FRACTIONAL CALCULUS OPERATORS; FUKUHARA EQUATION; INDEX LAW; NON-FUCHSIAN DIFFERENTIAL EQUATIONS; TRICOMI EQUATIONS; WHITTAKER EQUATIONS;

DIFFERENTIAL EQUATIONS;

EID: 0041703882     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(03)90007-1     Document Type: Article

References (28)

1. R. Hilfer, Editor, Applications of Fractional Calculus in Physics, World Scientific, Singapore, (2000).
2. I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, Volume 198, Academic Press, New York, (1999).
3. S.-T. Tu, D.-K. Chyan and H.M. Srivastava, Some families of ordinary and partial fractional differintegral equations, Integral Transform. Spec. Funct. 11, 291-302, (2001).
4. 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, 405-421, (2002).
5. 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, 35-43, (2001).
6. 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, 223-233, (2002).
7. 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, 49-60, (2002).
8. 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, 103-110, (2000).
9. S.-T. Tu, S.-D. Lin, Y.-T. Huang, and H.M. Srivastava, Solutions of a certain class of fractional differ integral equations, Appl. Math. Lett. 14 (2), 223-229, (2001).
10. K. Nishimoto, Fractional Calculus, Volume I, Descartes Press, Koriyama, (1984).
11. K. Nishimoto, Fractional Calculus, Volume II, Descartes Press, Koriyama, (1987).
12. K. Nishimoto, Fractional Calculus, Volume III, Descartes Press, Koriyama, (1989).
13. K. Nishimoto, Fractional Calculus, Volume V, Descartes Press, Koriyama (1991).
14. K. Nishimoto, Fractional Calculus, Volume V, Descartes Press, Koriyama, (1996).
15. K. Nishimoto, An Essence of Nishimoto's Fractional Calculus (Calculus of the 21st Century): Integrations and Differentiations of Arbitrary Order, Descartes Press, Koriyama (1991).
16. ν method to nonhomogeneous Gauss and Bessel equations, J. Fract. Calc. 9, 1-15, (1996).
17. ν method to nonhomogeneous Fukuhara equations. I, J. Fract. Calc. 9, 23-31 (1996).
18. ν method to nonhomogeneous and homogeneous Whittaker equations. I, J. Fract. Calc. 9, 17-22, (1996).
19. K. Nishimoto, S. Salinas de Romero, J. Matera and A.I. Prieto, N-method to the homogeneous Whittaker equations, J. Fract. Calc. 15, 13-23 (1999).
20. K. Nishimoto, S. Salinas de Romero, J. Matera and A.I. Prieto, N-method to the homogeneous Whittaker equations (Revise and supplement), J. Fract. Calc. 16, 123-128, (1999).
21. M. Fukuhara, Ordinary Differential Equations, Volume II, (in Japanese), Iwanami Shoten, Tokyo, (1941).
22. ν method to nonhomogeneous and homogeneous Whittaker equations. II (Some illustrative examples), J. Fract. Calc. 12, 29-35, (1997).
23. 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, 11-21, (2000).
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, Cambridge University Press, Cambridge, (1927).
25. A. Erdély, W. Magnus, F. Oberhettinger and F.G. Tricomi, Higher Transcendental Functions, Volume I, McGraw-Hill, New York, (1953).
26. F. G. Tricomi, Funzioni Ipergeometriche Confluenti, Edizioni Cremonese, Rome, (1954).
27. G.N. Watson, A Treatise on the Theory of Bessel Functions, Second Edition, Cambridge University Press, Cambridge, (1944).
28. ν method applied to some second order nonhomogeneous equations, J. Fract. Calc. 16, 85-97, (1999).