The Double Laplace-Stieltjes Transform and their Applications in solving Integral and partial Differential Equations
Keywords:
Laplace-Stieltjes Transform, Double Laplace Transform, Double Riemann-Stieltjes IntegralAbstract
Most phenomena in nature are represented using ordinary or partial differential equations which are easy to solve when combined with double integral transforms, Therefore, We find many previous studies talking about double integral transformations, the most famous of which is the double Laplace transform and the double Milline transform. In our research, we present a new double transform of a special nature, which is the double Laplace-Stieltjes transform, where we are found the relationship between it and the double Laplace transform, in addition to proving some of its properties and applying them in finding solutions to partial Differential equations and Integral Equations.
References
R. S. Dahiya and J. Saberi-Nadjafi, “Theorems on N - dimensional Laplace transforms and their applications”, 15th annual Conference of Applied Mathematics, Univ. of Central Oklahoma. Electronic Journal of Differential Equations, Conference 02, 61-74, 1999.
L. Debnath, “The Double Laplace Transforms and Their properties with Applications to Functional, Integral and Partial Differential equations”, Int. J. Appl. Comput. Math, 2, pp. 223-241, 2016.
D. Loonker, “Solution of Integral Equations and Laplace-Stieltjes Transform”, Palestine Journal of Mathematics, Vol. 5(1), pp.43-49, 2016.
F. Moricz, “order of magnitude of double fourier coefficients of functions of bounder variation”, Analysis (Munchen) 22 pp. 335-345, 2002.
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