TY - JOUR
T1 - Solving Fractional Nonlinear Fredholm Integro-differential Equations via Hybrid of Rationalized Haar Functions
AU - Yadollah Ordokhani and Neda Rahimi
JO - Journal of Information and Computing Science
VL - 3
SP - 169
EP - 180
PY - 2024
DA - 2024/01
SN - 9
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jics/22577.html
KW -  Fredholm  integro-differential  equation,  Riemann-Liouville  integral,  Caputo  fractional 
derivative,  Fractional operational matrix, Rationalized Haar, Hybrid. 

AB -  This  paper  presents  hybrid  of  rationalized  Haar  (HRH)  functions  method  for  approximate  the 
numerical  solution  of  the  fractional  nonlinear  Fredholm  integro-differential  equations  (FNFIDEs).  The 
fractional derivatives are considered in the sense of Caputo.  The  fractional operational  matrix of hybrid of 
block-pulse  and  rationalized  Haar  functions  are  presented.  This  matrix  together  with  the  dual  operational 
matrix are used to reduce the computation of FNFIDEs into a system of algebraic equations. Some numerical 
examples are given and the results of applying this method demonstrate time and computational are small.