On the Use of Aboodh Transform for Solving Non-integer Order Dynamical Systems

Abstract

In this research study, a transform technique called the Aboodh transform has been employed to find closed form solutions of initial value problems in non-integer order ordinary differential equations. A newly derived theorem in the present study provides a general structure for finding the exact solutions of such non-integer order problems to be solved by this transform technique. Upon comparison with existing transforms including Laplace, Mellin, Sumudu and Elzaki, the Aboodh transform can be found in good agreement. Various non-integer order differential equations including Bagley-Torvik type equation have successfully been solved by the Aboodh transform technique.