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Initial stress effects on fractional thermoelastic wave propagation in semiconductor media under three thermoelasticity theories. [PDF]
Ramadan ME +5 more
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Stability analysis and exploration of multiform soliton solutions for extended fractional NLS model using modified extended direct algebraic method. [PDF]
Soliman M +3 more
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ON HADAMARD FRACTIONAL CALCULUS
Fractals, 2017This paper is devoted to the investigation of the Hadamard fractional calculus in three aspects. First, we study the semigroup and reciprocal properties of the Hadamard-type fractional operators. Then, the definite conditions of certain class of Hadamard-type fractional differential equations (HTFDEs) are proposed through the Banach contraction ...
Ma, Li, Li, Changpin
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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,
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Applied Mathematics and Computation, 2015
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Discretized Fractional Calculus
SIAM Journal on Mathematical Analysis, 1986Es werden für Fraktionalintegrale der Form \(\int^{x}_{0}(x- s)^{\alpha -1}x^{\beta -1}g(x)ds\) Konvolutionsquadraturen untersucht, d.h. numerische Näherungen in den Punkten \(x=0,h,2h,...Nh\) bestimmt. Es wird gezeigt, daß die angegebenen Methoden konvergent von der Ordnung p sind, wenn sie stabil und von der Ordnung p konsistent sind.
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The differentiability in the fractional calculus
Nonlinear Analysis, 2001Summary: In this work we give a general concept of differentiability of order \(\alpha\in]0,1]\) for functions of one variable, and then for functions of several variables, in the sense of Nishimoto's fractional calculus.
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Essentials of Fractional Calculus
2015Essentials of fractional calculus are presented. Different kinds of integral and differential operators of fractional order are discussed. The notion of the Riemann-Liouville fractional integral is introduced as a natural generalization of the repeated integral written in a convolution type form.
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An application of the fractional calculus. IV
1984[For part III see the author in J. Korean Math. Soc. 20, 133-140 (1983; Zbl 0558.30017).] The class A(\(\alpha)\) of analytic functions \(f(z)=z+\sum^{\infty}_{n=2}a_ nz^ n\) which satisfy \(| (f(z)/z)-1|
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