Wavelet‎-based numerical ‎method‎ ‎‎‎‎for solving fractional integro-differential equation with a weakly singular ‎kernel

Document Type : Research Paper


1 Department of Mathematics‎, ‎University of ‎Hormozgan‎, ‎P‎. ‎O‎. ‎Box 3995‎, ‎Bandarabbas‎, ‎Iran

2 Department of Biomedical Sciences and Morphological and Functional Imaging‎,‎ University of Messina‎, ‎via Consolare Valeria 1‎, ‎98125 MESSINA‎, ‎Italy



This paper describes and compares application of wavelet basis and Block-Pulse functions (BPFs) for solving fractional integro-differential equation (FIDE) with a weakly singular kernel‎. ‎First‎, ‎a collocation method based on Haar wavelets (HW)‎, ‎Legendre wavelet (LW)‎, ‎Chebyshev wavelets (CHW)‎, ‎second kind Chebyshev wavelets (SKCHW)‎, ‎Cos and Sin wavelets (CASW) and BPFs are presented for driving approximate solution FIDEs with a weakly singular kernel‎. ‎Error estimates of all proposed numerical methods are given to test the convergence and accuracy of the method‎. ‎A comparative study of accuracy and computational time for the presented techniques is given‎.


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