On the Airy functions, Airy transform with applications

Abstract

Abstract. In the present work, the author studied some properties of the modified Bessel’s functions and Airy functions. It is worth mentioning that the Airy functions are used in many fields of physics. In many branches of classical and quantum physics, Airy functions are applied. We have also studied certain properties of the Airy transform and derive some new integral relations involving the Airy functions. We also provide a solution to non-linear Riccati differential equation in terms of the Airy functions. Non-trivial illustrative examples are also provided. All the results have been presented in lucid and easy language.