A Further Generalization of the General Polynomial Transform and its Basic Characteristics and Applications

In this article , we developed the general polynomial transform into a new transform ( Ahmad - Emad - Murat transform ) , which was expanded by writing a general formula of the Kernel function K ( x , t ) . Besides , we presented the essential characteristics and theorems of AEM transform and made new results. In addition , the efficiency of the proposed transform was verified by applying it to a set of important examples , the most important one is “ Cauchy Euler problems ” . The main advantage of the proposed transform is getting a more generalized transform and making it easier to handle in solving differential equations with variable coefficients , reducing effort and time in the calculations . Hence , the polynomial integral transform and general polynomial transform that have been introduced during the last years are special transforms of the AEM transform .