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This work is motivated essentially by the success of the applications of the nonsingular Yang–Abdel–Aty–Cattani (YAC) derivative in many research area of science, engineering, and financial mathematics. Furthermore, the major determination of this survey work is to achieve Fourier transform of the aforesaid new operator. Obviously, the Cauchy‐reaction diffusion equations have an important role in constructing well‐known models in some fields of science and engineering. Due to this motivation, we applied the aforesaid Robotnov fractional–exponential function‐based new fractional derivative to the Cauchy‐reaction diffusion equations and analyzed the proposed model analytically and graphically by using the generalized differential transform and residual power series methods. Finally, results obtained by the aforesaid proposed methods are found to be in excellent compliance with the known exact solutions. Three numerical examples are considered and described for the accuracy of the results. [ABSTRACT FROM AUTHOR]

In this work, we study the asymptotic properties of a new Sturm-Liouville problem with retarded argument. Contrary to previous works, differential equation includes eigenparameter as a quadratic function. In the considered problem arise new difficulties. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]