International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 8, Pages 1155-1170

Solution of Volterra-type integro-differential equations with a generalized Lauricella confluent hypergeometric function in the kernels

R. K. Saxena1 and S. L. Kalla2

1Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur 342004, India
2Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

Received 1 March 2005

Copyright © 2005 R. K. Saxena and S. L. Kalla. 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.


The object of this paper is to solve a fractional integro-differential equation involving a generalized Lauricella confluent hypergeometric function in several complex variables and the free term contains a continuous function f(τ). The method is based on certain properties of fractional calculus and the classical Laplace transform. A Cauchy-type problem involving the Caputo fractional derivatives and a generalized Volterra integral equation are also considered. Several special cases are mentioned. A number of results given recently by various authors follow as particular cases of formulas established here.