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Jhenrique
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If the gradient of f is equal to differential of f wrt s: [tex]\vec{\nabla}f=\frac{df}{d\vec{s}}[/tex] so, what is the curl of f and the gradient of f in terms of fractional differentiation?
Matterwave said:Edit: I have no idea why the f is boldfaced in the gradient formula...and I don't know how to fix it. It should be non-boldfaced as it's a functinon.
Matterwave said:I'm not sure what you mean by "fractional differentiation" (wikipedia has a definition that seems very different than what you're talking about here), but these three operations are all related to the exterior derivative (if that's what you were talking about) [itex]\bf{d}[/itex].
Matterwave said:Oh, so you mean like...
$$\nabla\cdot\vec{f}=\frac{\partial f_x}{\partial x}+\frac{\partial f_y}{\partial y}+\frac{\partial f_z}{\partial z}$$
?
Then your definition is at odds with how the term is already used, which has nothing to do with the derivative appearing in the form of a fraction. See this article on fractional derivatives.Jhenrique said:Fractional differentiation means, for me, express a derivative in the form of a fraction.
Differentiation is a mathematical process used to calculate the rate of change of a function at a specific point. It involves finding the derivative, or slope, of a function at a given point.
Differential operators are mathematical symbols or operations that are used to calculate derivatives. They are used to manipulate functions to find their derivatives, and they include operations such as differentiation, integration, and partial differentiation.
Differentiation is the process of finding the derivative of a function, while integration is the process of finding the area under a curve. In other words, differentiation deals with rates of change, while integration deals with accumulation and finding the total value of a function.
Differentiation is used in various fields such as physics, economics, and engineering to analyze and model real-life situations. For example, it can be used to calculate the velocity of an object, the rate of change of a stock price, or the slope of a curve in a road design.
Differential operators have many applications in mathematics, physics, and engineering. Some common applications include solving differential equations, finding extrema of functions, and modeling physical systems such as heat flow and fluid mechanics.