In the field of engineering technology, many problems can be transformed into the first kind
Fredholm integral equation, which has a prominent feature called “ill-posedness”. This …

This paper presents a numerical method for solving a certain class of Fredholm integral
equations of the first kind, whose unknown function is singular at the end-points of the …

In this paper, a new numerical algorithm for solving the time fractional convection–diffusion
equation with variable coefficients is proposed. The time fractional derivative is estimated …

In this paper, a semi-discrete scheme is presented for solving fourth-order partial integro-
differential equations with a weakly singular kernel. The second-order backward difference …

The book presents efficient numerical methods for simulation and analysis of physical
processes exhibiting fractional order (FO) dynamics. The book introduces FO system …

This study investigates a numerical method based on the Jacobi–Gauss quadrature for
solving Fredholm integral equations of the first kind with a weakly singular kernel by …

The main aim of this work is the use of a semi analytical method to obtain series solution of
Volterra and Fredholm integral equations of the second kind, the method so-called …

The theory of integral equations has been an active field of research for many years and is
inextricably related with other areas of Mathematics such as complex and mathematical …

Numerical schemes for nonlinear weakly singular Volterra and Fredholm integral equations
of the first kind are rarely investigated in the literature. In this paper, we present numerical …

We consider Fredholm integral equations of the first kind with symmetric kernels and use
Tikhonov's regularization property to transform them into second kind Fredholm equations …