A note on a class of singular integro-differential equations
نویسنده
چکیده
in which ak'S and bk'S are complex constants,fk(x) represents the kth derivative of the unknown function f(x) with prescribed initial valuesfk(0), along with the conditions thatfk(oo) = 0, for k = 0, 1, 2 . . . . . n, and 9(x) represents a known differentiable function arises in a natural way while solving a class of mixed boundary value problems of mathematical physics (see [-3, 5, 6]). Varley and Walker [7] have discussed a general method of solving (i.1) by converting it to a singular integral equation of second kind with a Cauchy Kernel, and have discussed a method of solution of the resulting singular integral equation which avoids the complication (see [4]) of calculating various singular integrals appearing in the final form of the solution. In the present investigation, we have employed a straightforward analysis which simplifies the work of Varley and Walker I-7] slightly and demonstrates clearly the underlying difficulties. A detailed procedure is explained to examine (1.1) for its solution under the assumptions that
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