Jñānābha, Vol. 50 (2) (2020), (84-92)
APPLICATION IN INITIAL VALUE PROBLEMS VIA OPERATIONAL TECHNIQUES ON A CONTOUR INTEGRAL FOR SRIVASTAVA - DAOUST FUNCTION OF TWO VARIABLES
By
Hemant Kumar
Department of Mathematics
D. A-V. Postgraduate College Kanpur - 208001, Uttar Pradesh, India
Email: palhemant2007@rediffmail.com
(Received : May 27, 2020 ; Revised: August 13, 2020)
DOI: https://doi.org/10.58250/jnanabha.2020.50210
In this paper, we introduce the contour integrals for two variables functions namely as Srivastava - Daoust and generalized Kampé de Fériet functions and then, by the fractional and partial derivatives operational techniques, obtain their many results and relations for various special functions useful in quantum mechanical fields. Again then, apply them to solve the fractional calculus problems involving the initial values with the Caputo fractional derivatives and Riemann - Liouville fractional integrals.
2010 Mathematics Subject Classifications: 33C15, 33C20, 33C60, 26A33, 11M06.
Keywords and phrases: Two variables Srivastava - Daoust function and generalized Kampé de Fériet function, contour integral representations, Mittag - Leffler functions, operational techniques, Caputo fractional derivatives and Riemann fractional integrals.