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

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  • R. K. Saxena
  • S. L. Kalla

Abstract

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 ( Ï„ ) . 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.

Suggested Citation

  • R. K. Saxena & S. L. Kalla, 2005. "Solution of Volterra-type integro-differential equations with a generalized Lauricella confluent hypergeometric function in the kernels," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-16, January.
    • Handle: RePEc:hin:jijmms:374615
    DOI: 10.1155/IJMMS.2005.1155
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    Cited by:

    1. Kürt, Cemaliye & Fernandez, Arran & Özarslan, Mehmet Ali, 2023. "Two unified families of bivariate Mittag-Leffler functions," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    2. Jessica Mendiola-Fuentes & Eugenio Guerrero-Ruiz & Juan Rosales-García, 2024. "Multivariate Mittag-Leffler Solution for a Forced Fractional-Order Harmonic Oscillator," Mathematics, MDPI, vol. 12(10), pages 1-11, May.

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