OICC Press Mathematical Analysis and its Contemporary Applications 5 4 2023 10 01 Solution of an infinite system of fractional differential equations in tempered sequence space 10.30495/maca.2023.2009474.1085 EN Rahul Rahul PDPM-Indian Institute of Information Technology, Design and Manufacturing Jabalpur-482005, India Sukanta Halder PDPM-Indian Institute of Information Technology, Design and Manufacturing Jabalpur-482005, India Nihar Kumar Mahato PDPM-Indian Institute of Information Technology, Design and Manufacturing Jabalpur-482005, India Journal Article 2023 10 01 In this article, we study an infinite system of fractional differential equations involving a generalized Caputo-Fabrizio fractional operator. By using Darbo’s fixed point theorem and the concept of measure of noncompactness, we establish the existence of a solution for the proposed system in tempered sequence space. Suitable examples are given to strengthen our article. At the end, we give an iterative algorithm using the homotopy perturbation method and Adomian decomposition method to solve our given example with high accuracy.