Mixed type of Fredholm-Volterra integral equation

Abstract

In this paper, under certain conditions, the solution of mixed type of Fredholm-Volterra integral equation is discussed and obtained in the space L_2 (−1, 1) × C[0, T ], T . Here, the singular part of kernel of Fredholm-Volterra integral term is established in a logarithmic form, while the kernel of Fredholm-Volterra integral term is a positive continuous function in time and belongs to the class C[0, T ], T . The solution, when the mixed type integral, takes a system form of Fredholm integral equation of the first or second kind are discussed.

Keywords

• Fredholm-Volterra integral equation
• Contact problem
• Chebyshev polynomial
• Logarithmic kernel
• Potential theory method