Convergence analysis of the product integration method for solving the fourth kind integral equations with weakly singular kernels

An efficient numerical method based on ultraspherical polynomials for linear weakly singular fractional Volterra integro‐differential equations

“…In this section, we recall Lemma 1 from previous research [28,42,44] and introduce a new lemma as a result of Lemma 2 from [42]. We aim to determine the overestimate for ||e|| L 2 w (−1,1) .…”

“…In this section, we recall Lemma 1 from previous research [28, 42, 44] and introduce a new lemma as a result of Lemma 2 from [42]. We aim to determine the overestimate for $$$ {\left\Vert e\right\Vert}_{L_w^2\left(-1,1\right)} $$$.…”

“…The weakly singular fractional integro‐differential equations appear in the mathematical modeling of many physical problems such as polymer physics and biophysics[1], heat conduction problems [3], and radiative equilibrium [4]. In recent years, several numerical methods have been presented to numerical solution of the integral equations, especially the fractional equations (see, e.g., earlier studies [5–35]).…”

A numerical study on the non‐smooth solutions of the nonlinear weakly singular fractional Volterra integro‐differential equations

“…In recent years, due to the many applications of fractional calculus in modeling natural phenomena, much attentions have been paid to the numerical solution of the fractional equations (see, e.g., previous studies 4–24 ).…”