This book is about the simulation and modeling of novel chaotic systems within the frame of fractal-fractional operators. The methods used, their convergence, stability, and error analysis are given, and this is the first book to offer mathematical modeling and simulations of chaotic problems with a wide range of fractal-fractional operators, to find solutions. Numerical Methods for Fractal-Fractional Differential Equations and Engineering: Simulations and Modeling provides details for stability, convergence, and analysis along with numerical methods and their solution procedures for fractal-fractional operators. The book offers applications to chaotic problems and simulations using multiple fractal-fractional operators and concentrates on models that display chaos. The book details how these systems can be predictable for a while and then can appear to become random. Practitioners, engineers, researchers, and senior undergraduate and graduate students from mathematics and engineering disciplines will find this book of interest._

Photoelectrochemical Bioanalysis: Fundamentals and Emerging Applications covers the fundamentals from a basic to advanced level, along with the latest accounting of emerging applications. As photoelectrochemical bioanalysis is a rapidly developing area with a wide range developments occurring alongside, it can be difficult for beginners to grasp the understanding of the ever-growing and continuously expanding body of knowledge. Sections detail information on applications in bioanalysis, their working principles, the methodologies of constructions and the approaches adopted with their respective advantages and disadvantages. This book will assist researchers in understanding the latest advances in the materials and engineering aspects of PCE bioanalysis. It also provides researchers with an overview of modern strategies applied for the performance enhancement of PCE materials as well as the modifications suggested to improve the potential of PCE bioanalytical techniques. Last but not least, it will assist researchers in finding gaps and potential opportunities in the field to impart novelty in their research

The study was conducted on the wheat crop for the management of aphids in the research area of University of Agriculture, Faisalabad during 2009. Fedding efficacy of various larval instars and adult of C. Septempunctata L. was studied under laboratory conditions of Biodiversity and Biosystematics Lab. Department of Agri- Entomology university of Agriculture, Faisalabad. The results revealed that the fourth larval of C. Septempunctata L. consumed more aphids (36.67) followed by third (30.32), second (16.47) and first instars (2.10) respectively. Whereas the adult of C. Septempunctata L. was found very much voracious and consumed 74.07 aphids. All the insecticides were statistically equal, in controlling the population of aphids. However Advantage caused more mortality followed by Acelan, Imidacloprid, Black Warent and Rigorous in field conditions. All the insecticides were also tested against aphid in controlled conditions of labs. The effects of these insecticides were statistically equal. However However Advantage caused more mortality followed by Acelan, Imidacloprid, Black Warent and Rigorous in field conditions.