Applied Mathematics & Information Sciences

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The main goal of this work is to introduce a new double transform named the double ARA-Formable transform (DARA- FT) we introduce the application of the new double transform to various fundamental functions and master properties. Additionally, we state and prove the convolution and existence theorems. Subsequently, by utilizing these findings, different kinds of partial differential equations (PDEs) are solved. We establish novel methods for resolving families of PDEs. With the latter, one can obtain precise answers to some well-known PDEs, including the telegraph equation, the advection-diffusion equation, the Klein-Gordon equation, and others. The results demonstrate the double ARA-Formable transform is effective and beneficial for handling these types of problems

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