Fredholm-Volterra integral equation and generalized potential kernel

Authors:
M. A. Abdou
Affiliations:
Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt
Venue:
Applied Mathematics and Computation
Year:
2002

Citing 5
Cited 2

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Abstract

A method is used to solve the Fredholm-Volterra integral equation of the first kind in the space L2(Ω) × C(0, T), Ω = { (x,y) ∈ Ω: √ x2 + y2 ≤ a, z = 0 } and T . The kernel of the Fredholm integral term considered in the generalized potential form belongs to the class C([Ω] × [Ω), while the kernel of the Volterra integral term is a positive and continuous function which belongs to the class C[0, T). Also in this work the solution of the Fredholm integral equation of the first and second kind with a generalized potential kernel is discussed. Many interesting cases are derived and established from the work.