Volterra Integral Equations with Gaussian Hypergeometric Function in the Kernel and Their Application to the Boundary Value Problems

Many problems of applied mathematics are reduced to the solution of integral equations with special functions in kernels, therefore the inversion formulas for such equations play an important role in solving various problems. In this paper the inversion formulas found are applied to solving Cauchy–Goursat problems for generalized Euler–Poisson–Darboux equation with the negative parameters. As an application of the results obtained explicit solutions of the problems posed are applied to finding functional relationships between the traces of the desired solution and its derivative brought to the line of degeneracy from the hyperbolic part of the mixed domain.

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