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A note on fractional powers of first-order differential and difference operators in relation to fractional derivatives [PDF]
E-Journal of Analysis and Applied MathematicsThis paper concentrates on fractional derivatives and fractional powers of first-order differential and difference operators. It is illustrated how fractional derivatives are related to fractional powers of a first-order positive operator with boundary ...
Ramil Salimov
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Coupled systems of fractional equations related to sound propagation: analysis and discussion [PDF]
, 2012 In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in the ...
Diethelm K. +6 more
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The Fractional Orthogonal Derivative [PDF]
Mathematics, 2015 This paper builds on the notion of the so-called orthogonal derivative, where an n-th order derivative is approximated by an integral involving an orthogonal polynomial of degree n. This notion was reviewed in great detail in a paper by the author and Koornwinder in 2012.
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Aging and rejuvenation with fractional derivatives [PDF]
Physical Review E, 2004 We discuss a dynamic procedure that makes the fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment and divergent second moment, namely with the power index mu in the interval 2>ta yields ord=mu -2.
Aquino, Gerardo +3 more
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No Violation of the Leibniz Rule. No Fractional Derivative [PDF]
, 2013 We demonstrate that a violation of the Leibniz rule is a characteristic property of derivatives of non-integer orders. We prove that all fractional derivatives D^a, which satisfy the Leibniz rule D^(fg)=(D^a f) g + f (D^a g), should have the integer ...
Tarasov, Vasily E.
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Fractional Derivatives and the Fundamental Theorem of Fractional Calculus [PDF]
Fractional Calculus and Applied Analysis, 2020 In this paper, we address the one-parameter families of the fractional integrals and derivatives defined on a finite interval. First we remind the reader of the known fact that under some reasonable conditions, there exists precisely one unique family of the fractional integrals, namely, the well-known Riemann-Liouville fractional integrals.
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On the oscillation of Hadamard fractional differential equations
Advances in Difference Equations, 2018 Hadamard fractional derivatives are nonlocal fractional derivatives with singular logarithmic kernel with memory, and hence they are suitable to describe complex systems.
Bahaaeldin Abdalla, Thabet Abdeljawad
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Operational Calculus for the General Fractional Derivatives of Arbitrary Order
Mathematics, 2022 In this paper, we deal with the general fractional integrals and the general fractional derivatives of arbitrary order with the kernels from a class of functions that have an integrable singularity of power function type at the origin.
Maryam Al-Kandari +2 more
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On the ψ -Hilfer fractional derivative
Communications in Nonlinear Science and Numerical Simulation, 2018 28 ...
José Vanteler da C. Sousa +1 more
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E. R. LOVE TYPE LEFT FRACTIONAL INTEGRAL INEQUALITIES
Проблемы анализа, 2020 Here first we derive a general reverse Minkowski integral inequality. Then motivated by the work of E. R. Love [4] on integral inequalities we produce general reverse and direct integral inequalities.
G. A. Anastassiou
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