Some volterra-type fractional integro-differential equations with a multivariable confluent hypergeometric function as their kernel

Journal of Integral Equations and Applications

Volumn 17, Issue 2, 2005, Pages 199-217

  Srivastava, H M ^a   Saxena, R K ^b  

^a UNIVERSITY OF VICTORIA   (Canada)

^b JAI NARAIN VYAS UNIVERSITY   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 64449087667     PISSN: 08973962     EISSN: None     Source Type: Journal    
DOI: 10.1216/jiea/1181075324     Document Type: Article

References (30)

1. M. Abramowitz and I.A. Stegun, editors, Handbook of mathematical functions with formulas, graphs, and mathematical tables, Applied Math. Series 55, 7th Printing, National Bureau of Standards, Washington, DC, 1968.
2. A.H. Al-Shammery, S.L. Kalla and H.G. Khajah, A fractional generalization of the free electron laser equation, Fract. Calc. Appl. Anal. 2 (1999), 501 508.
3. A.H. Al-Shammery, On a generalized fractional integro-differential equation of Volterratype, Integral Transform. Spec. Funct. 9 (2000), 81 90.
4. L. Boyadjiev and S.L. Kalla, Series representations of analytic functions and applications, Fract. Calc. Appl. Anal. 4 (2001), 379 408.
5. L. Boyadjiev, S.L. Kalla and H.G. Kajah, Analytical and numerical treatment of a fractional integro-differential equation of Volterra-type, Math. Comput. Modelling 25 (12) (1997), 1 9.
6. G. Dattoli, L. Gianessi, L. Mezi, A. Torre and R. Caloi, FEL time-evolution operator, Nuclear Instr. Methods A 304 (1991), 541 544.
7. G. Dattoli, S. Lorenzutta, G. Maino, D. Tocci and A. Torre, Results for an integro-differential equation arising in a radiation evolution problem, in Proc. of Internat. Workshop on Dynamics of Transport in Plasmas and Charged Beams (Torino, Italy; July 1994), World Scientific Publ. Co., Singapore, 1995, pp. 202 221.
8. G. Dattoli, S. Lorenzutta, G. Maino and A. Torre, Analytical treatment of the high-gain free electron laser equation, Radiat. Phys. Chem. 48 (1996), 29 40.
9. A. Erdélyi, W. Magnus, F. Oberhettinger and F.G. Tricomi, Higher transcendental functions, Vol. I, McGraw-Hill, New York, 1953.
10. A. Erdélyi, Tables of integral transforms, Volumes I, II, McGraw-Hill, New York, 1954.
11. C. Fox, The asymptotic expansion of generalized hypergeometric functions, Proc. London Math. Soc. (2) 27 (1928), 389 400.
12. R. Hilfer, ed., Applications of fractional calculus in physics, World Scientific Publ. Co., Singapore, 2000.
13. A.A. Kilbas, M. Saigo and R.K. Saxena, Solution of Volterra integrodifferential equations with generalized Mittag-Leffler function in the kernels, J. Integral Equations Appl. 14 (2002), 377 396.
14. M.L. Krasnov, A.I. Kiselëv and G.I. Makarenko, Integral equations, 3rd ed., Mir Publishers, Moscow, 1983.
15. A.M. Mathai and R.K. Saxena, Various practical problems in probability and statistics where Lauricella's confluent hypergeometric function appears naturally, Ganita Sandesh 1 (1987), 41 48.
16. K.S. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations, A Wiley-Intersci. Publ., John Wiley and Sons, New York, 1993.
17. K.B. Oldham and J. Spanier, The fractional calculus: Theory and applications of differentiation and integration to arbitrary order, Math. Sci. Engrg. 111, Academic Press, New York, 1974.
18. H.M. Ozaktas, Z. Zalevsky and M.A. Kutay, The fractional Fourier transform with applications in optics and signal processing,Wiley Ser. in Pure Applied Optics, John Wiley and Sons, New York, 2000.
19. I. Podlubny, Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Math. Sci. Engrg. 198, Academic Press, New York, 1999.
20. T.R. Prabhakar, A singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama Math. J. 19 (1971), 7 15.
21. L.B. Rall, Computational solution of nonlinear operator equations, Corrected reprint of the 1969 original (John Wiley and Sons, New York, 1969), Robert E. Krieger Publ. Co., Huntington, NY, 1979.
22. S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional integrals and derivatives: Theory and applications, Gordon and Breach Sci. Publ., Reading, 1993.
23. R.K. Saxena and S.L. Kalla, On a fractional generalization of the free electron laser equation, Appl. Math. Comput. 143 (2003), 89 97.
24. H.M. Srivastava, An integral equation involving the confluent hypergeometric function of several complex variables, Appl. Anal. 5 (1976), 251 256.
25. H.M. Srivastava, Remarks on some series expansions associated with certain products of the incomplete Gamma functions, Comput. Math. Appl. 46 (2003), 1749 1759.
26. H.M. Srivastava and R.G. Buschman, Theory and applications of convolution integral equations, Math. Appl. 79, Kluwer Acad. Publ., Dordrecht, 1992.
27. H.M. Srivastava and P.W. Karlsson, Multiple Gaussian hypergeometric series, Halsted Press, (Ellis Horwood Ltd., Chichester), John Wiley and Sons, New York, 1985.
28. H.M. Srivastava and B.R.K. Kashyap, Special functions in queuing theory and related stochastic processes, Academic Press, New York, 1982.
29. H.M. Srivastava and R.K. Saxena, Operators of fractional integration and their applications, Appl. Math. Comput. 118 (2001), 1 52.
30. E.M. Wright, The asymptotic expansion of the generalized hypergeometric function, I, II, J. London Math. Soc. 10 (1935), 286 293; Proc. London Math. Soc. (2) 46 (1940), 389 408.