اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدUniqueness of the fractional derivative definition
108
0
0.0
(
0
)
تأليف
Richard Herrmann
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
For the Riesz fractional derivative besides the well known integral representation two new differential representations are presented, which emphasize the local aspects of a fractional derivative. The consequences for a valid solution of the fractional Schroedinger equation are discussed.
قيم البحث
اقرأ أيضاً
We prove uniqueness for weak solutions to abstract parabolic equations with the fractional Marchaud or Caputo time derivative. We consider weak solutions in time for divergence form equations when the fractional derivative is transferred to the test function.
Accepting the Komar mass definition of a source with energy-momentum tensor $T_{mu u}$, and using the thermodynamic pressure definition, we find a relaxed energy-momentum conservation law. Thereinafter, we study some cosmological consequences of the
obtained energy-momentum conservation law. It has been found out that the dark sectors of cosmos are unifiable into one cosmic fluid in our setup. While this cosmic fluid impels the universe to enter an accelerated expansion phase, it may even show a baryonic behavior by itself during the cosmos evolution. Indeed, in this manner, while $T_{mu u}$ behaves baryonically, some parts of it, namely $T_{mu u}(e)$ which is satisfying the ordinary energy-momentum conservation law, are responsible for the current accelerated expansion.
Introducing a set ${alpha_i} in R$ of fractional exponential powers of focal distances an extension of symmetric Cassini-coordinates on the plane to the asymmetric case is proposed which leads to a new set of fractional generalized Cassini-coordinate
systems. Orthogonality and classical limiting cases are derived. An extension to cylindrically symmetric systems in $R^3$ is investigated. The resulting asymmetric coordinate systems are well suited to solve corresponding two- and three center problems in physics.
Forward amplitude analyses constitute an important approach in the investigation of the energy dependence of the total hadronic cross-section $sigma_{tot}$ and the $rho$ parameter. The standard picture indicates for $sigma_{tot}$ a leading log-square
d dependence at the highest c.m. energies, in accordance with the Froissart-Lukaszuk-Martin bound. Beyond this log-squared (L2) leading dependence, other amplitude analyses have considered a log-raised-to-gamma form (L$gamma$), with $gamma$ as a real free fit parameter. In this case, analytic connections with $rho$ can be obtained either through dispersion relations (derivative forms), or asymptotic uniqueness (Phragmen-Lindeloff theorems). In this work we present a detailed discussion on the similarities and mainly the differences between the Derivative Dispersion Relation (DDR) and Asymptotic Uniqueness (AU) approaches and results, with focus on the L$gamma$ and L2 leading terms. We also develop new Regge-Gribov fits with updated dataset on $sigma_{tot}$ and $rho$ from $pp$ and $bar{p}p$ scattering, in the region 5 GeV-8 TeV. The recent tension between the TOTEM and ATLAS results at 7 TeV and mainly 8 TeV is considered in the data reductions. Our main conclusions are: (1) all fit results present agreement with the experimental data analyzed and the goodness-of-fit is slightly better in case of the DDR approach; (2) by considering only the TOTEM data at the LHC region, the fits with L$gamma$ indicate $gammasim 2.0pm 0.2$ (AU) and $gammasim 2.3pm 0.1$ (DDR); (3) by including the ATLAS data the fits provide $gammasim 1.9pm 0.1$ (AU) and $gammasim 2.2pm 0.2$ (DDR); (4) in the formal and practical contexts, the DDR approach is more adequate for the energy interval investigated than the AU approach. A review on the analytic results for $sigma_{tot}$ and $rho$ from the Regge-Gribov, DDR and AU approaches is presented.
In this paper we investigate the solution of generalized distributed order diffusion equations with composite time fractional derivative by using the Fourier-Laplace transform method. We represent solutions in terms of infinite series in Fox $H$-func
tions. The fractional and second moments are derived by using Mittag-Leffler functions. We observe decelerating anomalous subdiffusion in case of two composite time fractional derivatives. Generalized uniformly distributed order diffusion equation, as a model for strong anomalous behavior, is analyzed by using Tauberian theorem. Some previously obtained results are special cases of those presented in this paper.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
