Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697713320230901Cubic hat-functions approximation for linear and nonlinear fractional integral-differential equations with weakly singular kernels5005314372210.22067/ijnao.2023.80249.1209ENH. EbrahimiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.0000-0003-0462-4729J. BiazarDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.0000-0001-8026-2999Journal Article20221225In the current study, a new numerical algorithm is presented to solve a class of nonlinear fractional integral-differential equations with weakly singular kernels. Cubic hat functions (CHFs) and their properties are introduced for the first time. A new fractional-order operational matrix of integration via CHFs is presented. Utilizing the operational matrices of CHFs, the main problem is transformed into a number of trivariate polynomial equations. Error analysis and the convergence of the proposed method are evaluated, and the convergence rate is addressed. Ultimately, three examples are provided to illustrate the precision and capabilities of this algorithm. The numerical results are presented in some tables and figures.https://ijnao.um.ac.ir/article_43722_e854731ae97a2dfa19bca6976f0d1067.pdf