Functional bounds and fractional calculus results for the Nuttall function

The importance of the Nuttall function in certain areas of applied science is a motivation to study their properties. The purpose of this paper is twofold. First, we aim at establishing a new several functional inequalities for the Nuttall function. As consequences, new functional bounds for the generalized Marcum Q-function are considered. Second, the fractional derivative and fractional integration formula involving the Nuttall function and some interesting special cases are discussed. Furthermore, to illustrate their accuracy of the obtained results, numerical computation and graphical representations are presented.