Some Fractional Operators with the Generalized Bessel-Maitland Function

In this paper, we aim to determine some results of the generalized Bessel-Maitland function in the field of fractional calculus. Here, some relations of the generalized Bessel-Maitland functions and the Mittag-Leffler functions are considered. We develop Saigo and Riemann-Liouville fractional integral operators by using the generalized Bessel-Maitland function, and results can be seen in the form of Fox-Wright functions. We establish a new operator L-nu,eta,rho,gamma,w,a+(mu,xi,m,sigma)phi and its inverse operator D-nu,eta,rho,gamma,w,a+(mu,xi,m,sigma)phi, involving the generalized Bessel-Maitland function as its kernel, and also discuss its convergence and boundedness. Moreover, the Riemann-Liouville operator and the integral transform (Laplace) of the new operator have been developed.