A New More General Integral Transform: Sharad Transform and Its Applications - Ugale, Sharad B.; Patil, Dinkar P. (Communications in Mathematics and Applications, 2024)
In this paper, we are presenting the new broad essential transform called the Sharad transform. Additionally, we demonstrated a few theorems and properties, similar to the linearity property and the convolution theorem. Additionally, we fostered a connection between the new transform and another old useful transform, similar to the Laplace transform, the Sumudu transform, the natural transform, the Elzaki transform, the Abhoodh transform, the Formable transform, and so forth. Here we presume that these transforms are the extraordinary instances of the new broad basic transform, the Sharad transform. This transform is applied to ordinary differential equations and partial differential equations. This transform will be utilised in the future to tackle a lot more the ordinary differential equations, the partial differential equations, integro-differential equations, fractional differential equations, difference equations, differential-difference equations, and so forth.
Keywords: Sharad transform; Laplace transform; Partial Differential Equation; Ordinary Differential Equation; Integral transform