Abstract
This paper is concerned to derive the main theorem of spectral relationships of Volterra–Fredholm integral equation (V-FIE) of the first kind in the space L2[−1,1]×C[0,T], −1⩽x⩽1, 0⩽t⩽T<1. The Fredholm integral (FI) term is considered in position and its kernel takes a logarithmic form multiplying by a continuous function. While Volterra integral (VI) term in time with a positive continuous kernel. Many important special and new cases can be established from the main theorem. Moreover, we use it to solve V-FIE of the second kind in the same space. The numerical results are computed and the error is calculated using Maple 12. Copyright © 2010 John Wiley & Sons, Ltd.
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