کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1891794 1043923 2012 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Extending the D’alembert solution to space–time Modified Riemann–Liouville fractional wave equations
موضوعات مرتبط
مهندسی و علوم پایه فیزیک و نجوم فیزیک آماری و غیرخطی
پیش نمایش صفحه اول مقاله
Extending the D’alembert solution to space–time Modified Riemann–Liouville fractional wave equations
چکیده انگلیسی

In the realm of complexity, it is argued that adequate modeling of TeV-physics demands an approach based on fractal operators and fractional calculus (FC). Non-local theories and memory effects are connected to complexity and the FC. The non-differentiable nature of the microscopic dynamics may be connected with time scales. Based on the Modified Riemann–Liouville definition of fractional derivatives, we have worked out explicit solutions to a fractional wave equation with suitable initial conditions to carefully understand the time evolution of classical fields with a fractional dynamics. First, by considering space–time partial fractional derivatives of the same order in time and space, a generalized fractional D’alembertian is introduced and by means of a transformation of variables to light-cone coordinates, an explicit analytical solution is obtained. To address the situation of different orders in the time and space derivatives, we adopt different approaches, as it will become clear throughout this paper. Aspects connected to Lorentz symmetry are analyzed in both approaches.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Chaos, Solitons & Fractals - Volume 45, Issue 6, June 2012, Pages 765–771
نویسندگان
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