Joint Natural and Fourier Transform Technique for Unified Fractional Schr�dinger Equation in Quantum Mechanics

Integral transform method play a significant role to solve different kinds of integral and differential equations of fractional order and integer order arise in several applications of engineering and physical sciences. Natural Transform converges to Laplace and Sumudu transforms. The aim of this present paper is to solve the unified fractional Schr�dinger equation occurs in the field of quantum mechanics. The solution is obtained by Natural transform technique for the Caputo fractional derivatives with time variable and Fourier transform for the Liouville fractional derivative with space variable. The result is provided in the computational form of the H-function. The paper explicitly reveals the efficiency and reliability of joint Natural and Fourier transform technique. Some special cases of the main result are mentioned. Achieved result is general in the nature and has capability of providing a number of known and new results. � The Electrochemical Society