TY - JOUR
ID - 43722
TI - Cubic hat-functions approximation for linear and nonlinear fractional integral-differential equations with weakly singular kernels
JO - Iranian Journal of Numerical Analysis and Optimization
JA - IJNAO
LA - en
SN - 2423-6977
AU - Ebrahimi, H.
AU - Biazar, J.
AD - Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.
Y1 - 2023
PY - 2023
VL - 13
IS - 3
SP - 500
EP - 531
KW - Fractional integral-differential equations
KW - Numerical algorithms
KW - Weakly singular kernels
KW - Cubic hat functions
KW - Fractional operational matrix
DO - 10.22067/ijnao.2023.80249.1209
N2 - In 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.
UR - https://ijnao.um.ac.ir/article_43722.html
L1 - https://ijnao.um.ac.ir/article_43722_e854731ae97a2dfa19bca6976f0d1067.pdf
ER -