A Constructive Approach to Generalized Integral Transforms

New approach to a generalized fractional integral

The paper presents a new fractional integration, which generalizes the Riemann-Liouville and Hadamard fractional integrals into a single form, which when a parameter fixed at different values, produces the above integrals as special cases. Conditions are given for such a generalized fractional integration operator to be bounded in an extended Lebesgue measurable space. Semigroup property for th...

Integral Transforms of Fourier Cosine and Sine Generalized Convolution Type

SOME INTEGRAL TRANSFORMS OF THE GENERALIZED k-MITTAG-LEFFLER FUNCTION

In the paper, the authors generalize the notion “k-Mittag-Leffler function”, establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function. 1. Preliminaries Throughout this paper, let C, R, R0 , R, Z − 0 , and N denote respectively the sets of com...

A Generalized Path Integral Control Approach to Reinforcement Learning

With the goal to generate more scalable algorithms with higher efficiency and fewer open parameters, reinforcement learning (RL) has recently moved towards combining classical techniques from optimal control and dynamic programming with modern learning techniques from statistical estimation theory. In this vein, this paper suggests to use the framework of stochastic optimal control with path in...

A Calderón–zygmund Estimate with Applications to Generalized Radon Transforms and Fourier Integral Operators

We prove a Calderón–Zygmund type estimate which can be applied to sharpen known regularity results on spherical means, Fourier integral operators, generalized Radon transforms and singular oscillatory integrals. The main theme in this paper is to strengthen various sharp L–Sobolev regularity results for integral operators. To illustrate this we consider the example of spherical means. Let σ den...