Vidya Patil

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

Fractional differential operators deal with derivatives of arbitrary order. In general the solution of a fractional differential equation involves the Mittag-Leffler function. In this paper we discuss the analytical and numerical solution of the fractional differential equation associated with the RLC electrical circuit, by applying the Caputo fractional differential operator. The solution obtained is expressed in terms of three parameter Mittag-Leffler function. Here we prove the existence and uniqueness of the solution to the fractional differential RLC electrical circuit and also provide numerical examples to show the accuracy and efficiency of the method used. � The Electrochemical Society