In this paper, using a generalized translation operator, we prove theestimates for the generalized Fourier-Bessel transform in the space L2 on certainclasses of functions.

In this paper we introduce a generalized Laplace transform in order to work with very general fractional derivative, and obtain the properties of new transform. We also include corresponding convolution inverse formula. particular, definition for improves previous results. Additionally, deal harmonic oscillator equation, showing that its allow one solve differential equations.

Introduction Whereas ordinary functions on a locally compact group map the group elements into the complex numbers, a stochastic process can be understood as a mapping into a Hilbert space. The idea of a generalized function is to reduce the knowledge about the function to that of certain averages. It leads to the concept of generalized functions as continuous linear functionals on spaces of te...

According to the theoretical results, the quantum searching algorithm can be generalized by replacing the Walsh-Hadamard(W-H) transform by almost any quantum mechanical operation. We have implemented the generalized algorithm using nuclear magnetic resonance techniques with a solution of chloroform molecules. Experimental results show the good agreement between theory and experiment. PACS numbe...

According to the theoretical results, the quantum searching algorithm can be generalized by replacing the Wash-Hadamard(W-H) transform by almost any quantum operator. We have implemented this generalized algorithm using nuclear magnetic resonance techniques with a solution of chloroform molecules. We find that experimental results represent a good agreement between theory and experiment. PACS n...