Solving Partial Differential Equations of Fractional Order by Using a Novel Double Integral Transform

In this work, the double Sumudu–Elzaki transform was used for solving fractional-partial differential equations (FPDEs) with starting and boundary conditions. We will use the fractional-order derivative (Caputo’s derivatives) idea. Theorems and facts that are crucial to the newly introduced transform are also discussed and illustrated. By using this newly designed integral transform and its properties, FPDEs can be reduced into algebraic equations. This strategy has the precise answer since it does not need any discrimination, transformation, or limited assumptions. Five further instances were given to support our conclusions. The results showed that the recommended strategy is superb, reliable, and efficient. It is also a simple method for solving specific problems in a number of applied scientific and technical fields.