University of Tabriz Computational Methods for Differential Equations 2345-3982 13 4 2025 10 01 Semi-analytical solutions for time-fractional Cauchy reaction-diffusion equations via the new Elazki transform iterative method 1201 1215 18544 10.22034/cmde.2024.53470.2253 EN Shivaji Ashok Tarate Department of Mathematics, New Arts, Commerce and Science College, Ahmednagar, Maharashtra, India. Ashok P Bhadane Department of Mathematics, Loknete Vyankatrao Hiray Arts, Science and Commerce College, Nashik, Maharashtra, India. Shrikisan B Gaikwad Department of Mathematics, New Arts, Commerce and Science College, Ahmednagar, Maharashtra, India. Kishor Ashok Kshirsagar Department of Mathematics, New Arts, Commerce and Science College, Ahmednagar, Maharashtra, India. Journal Article 2022 09 14 In this article, the estimated analytic solutions for time-fractional Cauchy Reaction-Diffusion Equations (CRDE) are obtained using a New Elzaki Transform Iterative Method (NETIM). This method is the fusion of the Elzaki transform and the Iterative approach. The proposed technique is elegant and easy to adopt and comprehend. The semi-analytical results demonstrate, as this paper shows, a graphical interpretation of the solution using the mathematical software “Mathematica Wolform” and considering Caputo’s sense derivatives to analytical results, the suggested strategy is efficient and straightforward https://cmde.tabrizu.ac.ir/article_18544_b9a08c4ca73a8849791515248f8ce757.pdf