کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5103486 | 1480105 | 2017 | 19 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Relaxation and diffusion models with non-singular kernels
ترجمه فارسی عنوان
مدل های آرامش بخش و انتشار با هسته های غیر انحصاری
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کلمات کلیدی
آرامش و انتشار ناهنجار، هسته غیرمجاز، هسته تابع نمایشی کشیده شده، مشخصه حافظه، میانگین جابه جایی مربع،
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
چکیده انگلیسی
Anomalous relaxation and diffusion processes have been widely quantified by fractional derivative models, where the definition of the fractional-order derivative remains a historical debate due to its limitation in describing different kinds of non-exponential decays (e.g. stretched exponential decay). Meanwhile, many efforts by mathematicians and engineers have been made to overcome the singularity of power function kernel in its definition. This study first explores physical properties of relaxation and diffusion models where the temporal derivative was defined recently using an exponential kernel. Analytical analysis shows that the Caputo type derivative model with an exponential kernel cannot characterize non-exponential dynamics well-documented in anomalous relaxation and diffusion. A legitimate extension of the previous derivative is then proposed by replacing the exponential kernel with a stretched exponential kernel. Numerical tests show that the Caputo type derivative model with the stretched exponential kernel can describe a much wider range of anomalous diffusion than the exponential kernel, implying the potential applicability of the new derivative in quantifying real-world, anomalous relaxation and diffusion processes.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica A: Statistical Mechanics and its Applications - Volume 468, 15 February 2017, Pages 590-596
Journal: Physica A: Statistical Mechanics and its Applications - Volume 468, 15 February 2017, Pages 590-596
نویسندگان
HongGuang Sun, Xiaoxiao Hao, Yong Zhang, Dumitru Baleanu,