Time-Space Fractional Heat Equation in the Unit Disk

We will study a maximal solution of the time-space fractional heat equation in complex domain. The fractional time is taken in the sense of the Riemann-Liouville operator, while the fractional space is assumed in the Srivastava-Owa operator. Here we employ some properties of the univalent functions in the unit disk to determine the upper bound of this solution. The maximal solution is illustrated in terms of the generalized hypergeometric functions

Content-Based Image Retrieval Based on Electromagnetism-Like Mechanism

Recently, many researchers in the field of automatic content-based image retrieval have devoted a remarkable amount of research looking for methods to retrieve the best relevant images to the query image. This paper presents a novel algorithm for increasing the precision in content-based image retrieval based on electromagnetism optimization technique. The electromagnetism optimization is a nature-inspired technique that follows the collective attraction-repulsion mechanism by considering each image as an electrical charge. The algorithm is composed of two phases: fitness function measurement and electromagnetism optimization technique. It is implemented on a database with 8,000 images spread across 80 classes with 100 images in each class. Eight thousand queries are fired on the database, and the overall average precision is computed. Experimental results of the proposed approach have shown significant improvement in the retrieval performance in regard to precision

On Generalized Fractional Differentiator Signals

By employing the generalized fractional differential operator, we introduce a system of fractional order derivative for a uniformly sampled polynomial signal. The calculation of the bring in signal depends on the additive combination of the weighted bring-in of N cascaded digital differentiators. The weights are imposed in a closed formula containing the Stirling numbers of the first kind. The approach taken in this work is to consider that signal function in terms of Newton series. The convergence of the system to a fractional time differentiator is discussed