In this paper, using the Schouten-Vanderpol and Titchmarsh theorems for the inverse Laplace transform, we obtain new integral identities for the Airy functions and their products. These integral identities are given in terms of the Laplace, Stieltjes and Hankel transforms.
In this article, the authors used two dimensional Laplace transform to solve non - homogeneous sub - ballistic fractional PDE and homogeneous systems of time fractional heat equations. Constructive examples are also provided.
In the present paper, time fractional partial differential equation is considered, where the fractional derivative is defined in the Caputo sense. Laplace transform method has been applied to obtain an exact solution. The authors solved certain homogeneous and nonhomogeneous time fractional heat equations using integral transform. Transform method is a powerful tool for solving fractional singular Integro -differential equations and PDEs. The result reveals that the transform method is very convenient and effective.
In this paper, using the integral identities of Bessel functions, we obtain new integral identities for the products of Airy functions. We get various integrals involving the Widder potential, the Fourier sine and cosine transforms of the products of Airy functions in terms of some special functions.
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