Laplace–Elzaki Transform and its Properties with Applications to Integral and Partial Differential Equations

Laplace-Elzaki transform (LET) as a double integral transform of a function 𝑓(𝑥,𝑡) of two variables was presented to solve some integral and partial differential equations. Main properties and theorems were proved. The convolution of two function 𝑓(𝑥,𝑡) and 𝑔(𝑥,𝑡) and the convolution theorem were discussed. The integral and partial differential equations were turned to algebraic ones by using (LET) and its properties. The results showed that the Laplace-Elzaki transform was more efficient and useful to handle such these kinds of equations.