Topic
Derivative
About: Derivative is a research topic. Over the lifetime, 1463 publications have been published within this topic receiving 15205 citations.
Papers published on a yearly basis
1 / 2
Papers
1 Jan 1992
TL;DR: In this paper, the authors present an example in two dimensions of a two-dimensional polynomial in terms of orthogonality, numerical integration, and functional spaces.
Abstract: Special Families of Polynomials.- Orthogonality.- Numerical Integration.- Transforms.- Functional Spaces.- Results in Approximation Theory.- Derivative Matrices.- Eigenvalue Analysis.- Ordinary Differential Equations.- Time-Dependent Problems.- Domain-Decomposition Methods.- Examples.- An Example in Two Dimensions.
438 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
1 Feb 1983
TL;DR: In this paper, the first six coefficients of a function which is inverse to a regular normalized univalent function whose derivative has a positive real part in the unit disk are used to find sharp bounds.
Abstract: Coefficient bounds for functions with a positive real part are used in a rather novel way to find sharp bounds for the first six coefficients of a function which is inverse to a regular normalized univalent function whose derivative has a positive real part in the unit disk.
283 citations
6 Mar 2020
TL;DR: The Caputo fractional derivative has been one of the most useful operators for modelling non-local behaviors by fractional differential equations as discussed by the authors. But it is not a suitable operator for modeling the Mittag-Leffler function.
Abstract: The Caputo fractional derivative has been one of the most useful operators for modelling non-local behaviours by fractional differential equations. It is defined, for a differentiable function f ( t ) , by a fractional integral operator applied to the derivative f ′ ( t ) . We define a new fractional operator by substituting for this f ′ ( t ) a more general proportional derivative. This new operator can also be written as a Riemann–Liouville integral of a proportional derivative, or in some important special cases as a linear combination of a Riemann–Liouville integral and a Caputo derivative. We then conduct some analysis of the new definition: constructing its inverse operator and Laplace transform, solving some fractional differential equations using it, and linking it with a recently described bivariate Mittag-Leffler function.
247 citations
1 Jan 1977
240 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 3 |
| 2021 | 98 |
| 2020 | 106 |
| 2019 | 100 |
| 2018 | 88 |
| 2017 | 55 |