Abstract
In the present paper, we discuss the solution of Euler-Darboux equation in terms of Dirichlet averages of boundary conditions on H?lder space and weighted H?lder spaces of continuous functions using Riemann-Liouville fractional integral operators. Moreover, the results are interpreted in alternative form.
Highlights
The subject of Dirichlet averages has received momentum in the last decade of 20th century with reference to the solution of certain partial differential equations
Not much work has been registered in this area of Applied Mathematics except some papers devoted to evaluation of Dirichlet averages of elementary functions as well as higher treanscendental functions interpreting the results in more general special functions
The present paper is ventured to give the interpretation of solution of a typical partial differential equation and prove its inclusion properties with respect to Hölder spaces
Summary
The subject of Dirichlet averages has received momentum in the last decade of 20th century with reference to the solution of certain partial differential equations. The present paper is ventured to give the interpretation of solution of a typical partial differential equation and prove its inclusion properties with respect to Hölder spaces. (2016) Dirichlet Averages, Fractional Integral Operators and Solution of Euler-Darboux Equation on Hölder Spaces. Deora and Banerji [6] represented the solution of Equation (2) in terms of Dirichlet averages of boundary condition functions given in (3) as follows u x, y. In the present paper we discuss the Dirichlet averages on Hölder Space via right-sided Riemann-Liouville fractional integral operators and prove the solution of Equation (2) to be justified on such spaces. In what follows are the preliminaries and definitions related to fractional integral operators, Dirichlet averages, and Hölder spaces of continuous functions
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