OICC Press Mathematical Analysis and its Contemporary Applications 6 4 2024 12 24 Hat functions operational matrix for solving the nonlinear fractional-order integro-differential equation 10.30495/maca.2024.720828 EN Amir Ahmad Khajehnasiri Department of Economics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran; Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran Journal Article 2024 12 24 This paper aims to construct a general formulation for the hat basis functions of the fractional integral operator. We derive the hat basis functions operational matrix of the fractional order integration, and use it to solve the fractional-order integro-differential equation. The method is described and illustrated with a numerical example. The results show that the method is accurate and easy to apply.