This study presents the nonconformable fractional Elzaki transform (NCFET) method. We used this method to solve various fractional differential equations (FDEs) with nonconformable fractional derivatives (NCFDs). We studied and proved the basic properties and advantages of this new method. We discussed some examples and conducted a comparative study, presenting exact results through graphs and tables. The results showed that the new method worked well, was easy to use, and could correctly solve several fractional differential equations, even those with nonconformable fractional derivatives.

In this paper, we used an efficient new technique for solving fractional partial and integral equations that meet specific criteria. This technique is referred to as the conformable double Sumudu-Elzaki transform (CDSET) and combines two well-known transforms, namely, the Sumudu transform, and the Elzaki transform. We attempt to present the fundamental concepts and findings of the recently suggested transformation. Relying on this brand-new integral transform and its related features, users can transform the equations above into algebraic equations that are easier to understand. Consequently, exact solutions can efficiently and rapidly be acquired. We conclude that the suggested approach is dependable and effective, as demonstrated. Therefore, it facilitates accurate and feasible solutions for other fractional linear models such as conformable derivatives.