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Analysis of Riccati Differential Equations within a New Fractional Derivative without Singular Kernel

Jafari H., Lia A., Tejadodi H., Baleanu D.

Fundamenta Informaticae

2017

Vol. 151, nr 1/4

161--171

Recently Caputo and Fabrizio suggested new definition of fractional derivative that the new kernel has no singularity. In this paper, an analytical method for solving Riccati differential equation with a new fractional derivative is reported. We present numerical results of solving the fractional Riccati differential equations by using the variational iteration method and its modification. The obtained results of two methods demonstrate the efficiency and simplicity of the MVIM that gives good approximations for a larger interval.

Rekreacja w dolinie rzeki na przykładzie małych dolin rzecznych Wrocławia

Lia A., Walter E.

Architektura Krajobrazu

2010

nr 2

24--33

In the contemporary world of intense, fast and unhealthy lifestyle, a need for recreation is increasing; it is supposed to smooth out the physical passivity of everyday life. The appearance of an open water source is one of the basic components deciding on attractiveness of a recreational-holiday area. Wroclaw is a city strongly shaped by its big river. Apart from the Odra there are four smaller rivers: the Widawa, the Bystrzyca, the Sleza and the Otawa. They influence the landscape of the city and its structure. Within the area of each of the rivers exist organized and half-natural areas of green, which do not fully exploit the potential of the closeness of the natural watercourse. The present article presents the research on the role of green areas within small river valleys of Wroclaw. The authors attempt to determine the directions of action, which will enable an increase in the recreational effectiveness of the studied areas, with special consideration to the potential of closeness of the river. The areas have been explored with respect to their recreational function by conducting analyses and assessments of the possibilities and degree of satisfy ing the needs of recreational inhabitants of these areas. A model of the relations drawn up by A. Lis (2005) has been used in the research.