Application of Fractional Calculus to Degenerate Hyperbolic Equations

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The research on definitions and properties of generalized fractional calculus, and the investigation on solutions of the Euler-Darboux equation as an application of the fractional calculus were already published. Further, various properties of hypergeometric functions, especially behavior of the functions near the boundaries of convergence regions, were reported. In 1991 and 1992, we have the following results : On relations of products of generalized fractional integrals with the Laplace and Stieltjes transforms in the generalized function space ; On the composition of the fractional integrals and axisymmetric differential operator in potential theory ; On the problem of mapping property by the fractional integrals of the convex and starlike functions in the theory of univalent functions ; On representability of the fractional integrals by products of the Mellin and the Laplace transforms ; On applications of the fractional calculus to the H-function ; On the relation of the fractional calculus with the Laplace transform ; On solutions of dual integral equations involving the fractional calculus ; On the definition and properties of the multidimensional modified fractional calculus ; On the establishment of new integral representation formulas for multidimensional hypergeometric series ; On new integral transforms with Meijer's G-function as kernels and their convolutions ; On the application of the fractional calculus to certain probabilistic density function with multidimensional hypergeometric functions ; On the behavior near boundaries of convergence regions of the Lauricella series F_S, F_T, the Srivastava series H_C, and the Horn series H_3, G_1, G_2 ; On estimations and mapping properties of operators with power-logarithmic kernel in the generalized Holder space ; On properties in the space L_<nu,p> of integral transforms with the H-function as kernel.