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Báo cáo hóa học: " Research Article From Newton’s Equation to Fractional Diffusion and Wave Equations"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article From Newton’s Equation to Fractional Diffusion and Wave Equations | Hindawi Publishing Corporation Advances in Difference Equations Volume 2011 Article ID 169421 13 pages doi 10.1155 2011 169421 Research Article From Newton s Equation to Fractional Diffusion and Wave Equations Luis Vazquez Departamento de Matemdtica Aplicada Facultad de Informdtica Universidad Complutense de Madrid 28040 Madrid Spain Correspondence should be addressed to Luis Vazquez lvazquez@fdi.ucm.es Received 12 December 2010 Accepted 18 February 2011 Academic Editor J. J. Trujillo Copyright 2011 Luis Vazquez. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Fractional calculus represents a natural instrument to model nonlocal or long-range dependence phenomena either in space or time. The processes that involve different space and time scales appear in a wide range of contexts from physics and chemistry to biology and engineering. In many of these problems the dynamics of the system can be formulated in terms of fractional differential equations which include the nonlocal effects either in space or time. We give a brief nonexhaustive panoramic view of the mathematical tools associated with fractional calculus as well as a description of some fields where either it is applied or could be potentially applied. 1. Introduction Fractional calculus see 1 offers a very suggestive and stimulating scenario where we have the convergence of deep and fundamental mathematical questions development of appropriate numerical algorithms as well as the applications to modelizations in different frameworks. An illustration of the physical applications of fractional calculus is the recent following books and special issues on applications on nanotechnology and other important topics 2-6 among many others. From a mathematical point of view the modelization of the long-range dependence is associated with integrodifferential