Topic
Total derivative
About: Total derivative is a research topic. Over the lifetime, 365 publications have been published within this topic receiving 7110 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this paper, the authors presented an efficient and reliable treatment of the homotopy perturbation method (HPM) for nonlinear partial differential equations with fractional time derivative, described in the Caputo sense.
417 citations
TL;DR: In this paper, the fractional complex transform is suggested to convert a fractional differential equation with Jumarie's modification of Riemann-Liouville derivative into its classical differential partner.
379 citations
TL;DR: This concept of ''memory-dependent derivative'', which is simply defined in an integral form of a common derivative with a kernel function on a slipping interval, is better than the fractional one for reflecting the memory effect.
Abstract: Enlightened by the Caputo type of fractional derivative, here we bring forth a concept of ''memory-dependent derivative'', which is simply defined in an integral form of a common derivative with a kernel function on a slipping interval. In case the time delay tends to zero it tends to the common derivative. High order derivatives also accord with the first order one. Comparatively, the form of kernel function for the fractional type is fixed, yet that of the memory-dependent type can be chosen freely according to the necessity of applications. So this kind of definition is better than the fractional one for reflecting the memory effect (instantaneous change rate depends on the past state). Its definition is more intuitionistic for understanding the physical meaning and the corresponding memory-dependent differential equation has more expressive force.
377 citations
TL;DR: This paper focuses on establishing stability theorems for fractional differential system with Riemann-Liouville derivative, in particular the analysis covers the linear system, the perturbed system and the time-delayed system.
233 citations
TL;DR: In this article, the authors revisited the results of Zamolodchikov and others on the deformation of two-dimensional quantum field theory by the determinant of the stress tensor, commonly referred to as $T\overline T$ Infinitesimally this is equivalent to a random coordinate transformation with a local action which is, however, a total derivative and therefore gives a contribution only from boundaries or nontrivial topology.
Abstract: We revisit the results of Zamolodchikov and others on the deformation of two-dimensional quantum field theory by the determinant $\det T$ of the stress tensor, commonly referred to as $T\overline T$ Infinitesimally this is equivalent to a random coordinate transformation, with a local action which is, however, a total derivative and therefore gives a contribution only from boundaries or nontrivial topology We discuss in detail the examples of a torus, a finite cylinder, a disk and a more general simply connected domain In all cases the partition function evolves according to a linear diffusion-type equation, and the deformation may be viewed as a kind of random walk in moduli space We also discuss possible generalizations to higher dimensions
194 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 13 |
| 2020 | 9 |
| 2019 | 11 |
| 2018 | 13 |
| 2017 | 15 |
| 2016 | 30 |