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This article is cited in 4 scientific papers (total in 4 papers)
Differential Equations
Generalized Integral Laplace Transform and Its Application to Solving Some Integral Equations
S. M. Zaikinaab a Volgograd State University, Volgograd, 400062, Russian Federation
b Samara State Technical University, Samara, 443100, Russian Federation
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
We present integral transforms $\widetilde {\mathcal L}\left\{f(t);x\right\}$ and $\widetilde {\mathcal L}_{\gamma_1,\gamma_2,\gamma} \left\{f(t);x\right\}$, generalizing the classical Laplace transform. The $(\tau, \beta)$- generalized confluent hypergeometric functions are the kernels of these integral transforms. At certain values of the parameters these transforms coincides with the famous classical Laplace transform. The inverse formula for the transforms is given. The convolution theorem for transform $\widetilde {\mathcal L}\left\{f(t);x\right\}$ is proven. Volterra integral equations of the first kind with core containing the generalized confluent hypergeometric function ${\mathstrut}_1\Phi{\mathstrut}_1^{\tau,\beta}(a;c;z)$ are considered. The above equation is solved by the method of integral transforms. The treatment of integral transforms is applied to get the desired solution of the integral equation. The solution is obtained in explicit form.
Keywords:
Laplace integral transform, integral equations, generalized hypergeometric function.
Original article submitted 30/IX/2013 revision submitted – 05/XII/2013
Citation:
S. M. Zaikina, “Generalized Integral Laplace Transform and Its Application to Solving Some Integral Equations”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(34) (2014), 19–24
Linking options:
https://www.mathnet.ru/eng/vsgtu1265 https://www.mathnet.ru/eng/vsgtu/v134/p19
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