Fractional Operators Associated with the Generalized Mittag-leffler Function in the Kernel
Chander Prakash Samar *
Department of Mathematics, Jaipur National University, (Raj.), India.
Abhishek Kumar Chaurasiya
Department of Mathematics, Jaipur National University, (Raj.), India.
Praveen Kumar Sherawat
Department of Mathematics, Jaipur National University, (Raj.), India.
*Author to whom correspondence should be addressed.
Abstract
This work is devoted to investigating fractional calculus involving integral and differential operators associated with the generalized Mittag-Leffler function in the kernel.
The results include differentiation and fractional calculus operators associated with the generalized Mittag-Leffler function. These outcomes are used to establish analogous properties and derive selected special cases. The relationship between the obtained results and earlier work is also explained.
Keywords: Fractional calculus, fractional integral operator, fractional differential operator, generalized Mittag-Leffler function, Riemann-Liouville operator, Hilfer operator, integral transforms, special functions, bounded operator, fractional kernel