Research ArticleOpen AccessGoogle Scholar indexed
Dirichlet Averages, Fractional Integral Operators and Solution of Euler-Darboux Equation on Hölder Spaces
Department of Basic & Applied Sciences, M. L. V. Textile & Engineering College, Bhilwara, India
- 1 Department of Basic & Applied Sciences, M. L. V. Textile & Engineering College, Bhilwara, India
Applied Mathematics·Volume 07 (2016)·Pages 1498–1503·Published 17 August 2016·DOI10.4236/am.2016.714129
Copy link · social · email
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.
KeywordsFractional Integral OperatorsDirichlet AveragesHölder Space
- Nahusev, A.M. (1969) A New Boundary Problem for a Degenerate Hyperbolic Equation. Soviet Mathematics Doklady, 10, 935-938.
- Saigo, M. (1979) A Certain Boundary Value Problem for the Euler-Darboux Equation. Mathematica Japonica, 24, 337-385.
- Saigo, M. (1979) A Certain Boundary Value Problem for the Euler-Darboux Equation-II. Mathematica Japonica, 25, 211-220.
- Saigo, M. (1981) A Certain Boundary Value Problem for the Euler-Darboux Equation-III. Mathematica Japonica, 26, 103-119.
- Srivastava, H.M. and Saigo, M. (1987) Multiplication of Fractional Calculus Operators and Boundary Value Problems Involving the Euler-Darboux Equation. Journal of Mathematical Analysis and Applications, 121, 325-369. http://dx.doi.org/10.1016/0022-247X(87)90251-4
- Deora, Y. and Banerji, P.K. (1994) An Application of Fractional Calculus to the Solution of Euler-Darboux Equation in Terms of Dirichlet Averages. Journal of Fractional Calculus, 5, 91-94.
- Kilbas, A.A., Repin, O.A. and Saigo, M. (1996) Solution in Closed Form of Boundary Value Problem for Degenerate Equation of Hyperbolic Type. Kyungpook Mathematical Journal, 36, 261-273.
- Carlson, B.C. (1969) A Connection between Elementary Functions and Higher Transcendental Functions. SIAM Journal on Applied Mathematics, 17, 116-148. http://dx.doi.org/10.1137/0117013
- Banerji, P.K. and Deora, Y. (1998) Laplace Transform of the Product of Two Generalized Laguerre Functions to Evaluate Averaged Functions. Bulletin of Calcutta Mathematical Society, 90, 389-394.
- Deora, Y. and Banerji, P.K. (1993) Double Dirichlet Average of ex Using Fractional Derivative. Journal of Fractional Calculus, 3, 81-86.
- Deora, Y. and Banerji, P.K. (1993) Triple Dirichlet Average and Fractional Derivative. Revista Técnica de la Facultad de Ingeniería Universidad del Zulia, 16, 157-161.
- Deora, Y., Banerji, P.K. and Saigo, M. (1994) Fractional Integral and Dirichlet Averages. Journal of Fractional Calculus, 6, 55-59.
- Gupta, S.C. and Agrawal, B.M. (1990) Dirichlet Averages and Fractional Derivatives. The Journal of the Indian Academy of Mathematics, 12, 103-115.
- Gupta, S.C. and Agrawal, B.M. (1991) Double Dirichlet Averages and Fractional Derivatives. Ganita Sandesh, 5, 47-53.
- Kattuvettill, A. (2008) On Dirichlet Averages. STARS: International Journal, 2, 78-88.