Abstract
This article discusses theory, properties, and applications of the novel integral transform known as -transform ( T) for fractional differential equations. Several fundamental theorems on fractional Riemann-Liouville and Caputo derivatives as well as proofs of some important results and functions are presented using the proposed transform. The exact and approximate solutions to numerous fractional differential equations (nonlinear Whitham- Broer-Kaup and KdV equations) are presented with numerical illustrations for validity, accuracy, and efficiency. It is observed that this fast-converging transform is a functional and valuable method to study a wide range of nonlinear problems in science and engineering.
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