This work discusses the beginning of fractional calculus and how Sumudu Elzaki transforms are applied to derivatives. approach combines a double Sumudu-Elzaki transform strategy discover analytic solutions space-time partial differential equations in Mittag-Leffler functions subject initial boundary conditions. Where this method gets closer correct answer, technique's efficacy is demonstrated u...

In this paper, a new Sumudu transform iterative method is established and successfully applied to find the approximate analytical solutions for time-fractional Cauchy reaction-diffusion equations. The approach is easy to implement and understand. The numerical results show that the proposed method is very simple and efficient.

The goal of this study is to suggest a new general triple integral transform known as Gamar transform. Next, we compare the current number existing transforms such those by Laplace, Sumudu, Elzaki, Aboodh, and Laplace–Aboodh–Sumudu. We outline its essential properties prove some important results, including linearity property, existence theorem, convolution derivatives properties. Moreover, pro...

In this paper, the new iterative method (NIM) is applied to solve nonlinear fractional gas dynamics equation. Further, a coupling of the Sumudu transform and Adomian decomposion (STADM) is used to get an approximate solution of the same problem. The results obtained by the two methods are found to be in agreement. Therefore, the NIM may be considered efficient method for finding approximate sol...

In this paper, we obtain the Sumudu transform of generalized composite fractional derivative and some lemmas related to inverse transform. Further, find solution nonlinear reaction diffusion equation with by applying Fourier transforms.