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Fractional Calculus, 2018
This paper aims to give the reader a comfortable introduction to Fractional Calculus. Fractional Derivatives and Integrals are defined in multiple ways and then connected to each other in order to give a firm understanding in the subject.
Richard Herrmann
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This paper aims to give the reader a comfortable introduction to Fractional Calculus. Fractional Derivatives and Integrals are defined in multiple ways and then connected to each other in order to give a firm understanding in the subject.
Richard Herrmann
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Fractal calculus and its geometrical explanation
Results in Physics, 2018 Ji-Huan He
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Lectures on the Geometry of Manifolds, 2020
Description: The three higher-dimensional versions of the fundamental theorem of calculus – Green's theorem, the divergence theorem, and Stokes' theorem – that one encounters in a typical multi-variable calculus course have two paradoxical ...
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Description: The three higher-dimensional versions of the fundamental theorem of calculus – Green's theorem, the divergence theorem, and Stokes' theorem – that one encounters in a typical multi-variable calculus course have two paradoxical ...
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The role of fractional calculus in modeling biological phenomena: A review
Communications in Nonlinear Science and Numerical Simulation, 2017Dana Copot
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Advances in Applied Clifford Algebras, 1998
The goal of the paper is to present a hyperbolic calculus which bases on so-called hyperbolic numbers and is related to Lorentz transformations and dilatations in the two-dimensional Minkowski space-time. The set of hyperbolic numbers is defined by \(P=\{t+hx:t,x\in\mathbb{R}\}\), \(h^2=1\).
Motter, A. E., Rosa, M. A. F.
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The goal of the paper is to present a hyperbolic calculus which bases on so-called hyperbolic numbers and is related to Lorentz transformations and dilatations in the two-dimensional Minkowski space-time. The set of hyperbolic numbers is defined by \(P=\{t+hx:t,x\in\mathbb{R}\}\), \(h^2=1\).
Motter, A. E., Rosa, M. A. F.
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A new collection of real world applications of fractional calculus in science and engineering
Communications in nonlinear science & numerical simulation, 2018Fractional calculus is at this stage an arena where many models are still to be introduced, discussed and applied to real world applications in many branches of science and engineering where nonlocality plays a crucial role.
Hongguang Sun +4 more
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Operational Calculus for the General Fractional Derivative and Its Applications
Fractional Calculus and Applied Analysis, 2021In this paper, we first address the general fractional integrals and derivatives with the Sonine kernels that possess the integrable singularities of power function type at the point zero.
Yuri Luchko
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Journal of Urology, 1985
Triamterene therapy is an unusual cause of nephrolithiasis and, when this agent is found in a stone, generally it is deposited in minor amounts. We report a renal calculus consisting mostly of triamterene and its 2 major metabolites in a patient taking a triamterene-containing drug, and discuss some implications.
E S, Dickstein, W D, Loeser
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Triamterene therapy is an unusual cause of nephrolithiasis and, when this agent is found in a stone, generally it is deposited in minor amounts. We report a renal calculus consisting mostly of triamterene and its 2 major metabolites in a patient taking a triamterene-containing drug, and discuss some implications.
E S, Dickstein, W D, Loeser
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Set-Valued and Variational Analysis, 2010
Consider a set-valued mapping \(F: X\twoheadrightarrow Z\) between Banach spaces \(X\) and \(Z\) with the dual spaces \(X^*\) and \(Z^*\), respectively. The basic \textit{coderivative} of \(F\) at \((\bar x, \bar z)\in \text{gph\;} F\) and \(z^*\in Z^*\) is given by \[ D^* F(\overline{x},\overline{z})(z^*):=\big\{x^*\in X^*\mid(x^*,-z^*)\in N\big ...
Li, Shengjie +2 more
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Consider a set-valued mapping \(F: X\twoheadrightarrow Z\) between Banach spaces \(X\) and \(Z\) with the dual spaces \(X^*\) and \(Z^*\), respectively. The basic \textit{coderivative} of \(F\) at \((\bar x, \bar z)\in \text{gph\;} F\) and \(z^*\in Z^*\) is given by \[ D^* F(\overline{x},\overline{z})(z^*):=\big\{x^*\in X^*\mid(x^*,-z^*)\in N\big ...
Li, Shengjie +2 more
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The Mathematical Gazette, 1936
1. Let f(x) be a real function of a real variable x . The meanings of when λ is a positive integer, a negative integer and zero, are well known. In the first case,
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1. Let f(x) be a real function of a real variable x . The meanings of when λ is a positive integer, a negative integer and zero, are well known. In the first case,
openaire +2 more sources