On the generalized Elzaki transform and its applications to fractional differential equations

In this paper, we introduce a modified Elzaki transform and its generalization, namely the Elzaki transform, and its own convolution theorem is given. These generalization are given by composition with a monotonic increasing function $ \varrho $ having a continuous derivative. A revised version of the Elzaki transform that is broader in scope and applicable over a wider range is developed, and some of its fundamental properties are given. This modified transform is performed to find solutions of certain non homogeneous linear $ \varrho $ Riemann–Liouville, $ \varrho $ Caputo fractional differential equations. Using comparision graphs, one can determine the effectiveness of the solutions. This research opens up new avenues for future research and has the potential to make a significant impact on the field of mathematics and its applications.