Analytical and numerical study for an integro-differential nonlinear volterra equation with weakly singular kernel

2018 ◽  
Vol 37 (4) ◽  
pp. 4661-4674 ◽  
Author(s):  
Mourad Ghiat ◽  
Hamza Guebbai
Keyword(s):  
Volterra Equation ◽  
Numerical Study ◽  
Singular Kernel ◽  
Weakly Singular Kernel ◽  
Weakly Singular

scholarly journals A numerical study on the non-smooth solutions of the nonlinear weakly singular fractional integro-differential equations

2021 ◽  
Author(s):  
Sayed Arsalan Sajjadi ◽  
Hashem Saberi Najafi ◽  
Hossein Aminikhah
Keyword(s):  
Lower Bound ◽  
Differential Equations ◽  
Caputo Derivative ◽  
Numerical Study ◽  
Singular Kernel ◽  
Smooth Solutions ◽  
Weakly Singular Kernel ◽  
Numerical Examples ◽  
Weakly Singular

The solutions of weakly singular fractional integro-differential equations involving the Caputo derivative have singularity at the lower bound of the domain of integration. In this paper, we design an algorithm to prevail on this non-smooth behaviour of solutions of the nonlinear fractional integro-differential equations with a weakly singular kernel. The convergence of the proposed method is investigated. The proposed scheme is employed to solve four numerical examples in order to test its efficiency and accuracy.

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