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Differential equations with tempered Ψ-Caputo fractional derivative
Mathematical Modelling and Analysis, 2021 In this paper we define a new type of the fractional derivative, which we call tempered Ψ−Caputo fractional derivative. It is a generalization of the tempered Caputo fractional derivative and of the Ψ−Caputo fractional derivative.
Milan Medveď, Eva Brestovanská
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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.
Enno Diekema
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No nonlocality. No fractional derivative [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2018 The paper discusses the characteristic properties of fractional derivatives of non-integer order. It is known that derivatives of integer orders are determined by properties of differentiable functions only in an infinitely small neighborhood of the considered point.
Vasily E Tarasov
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On the ψ -Hilfer fractional derivative
Communications in Nonlinear Science and Numerical Simulation, 2018 28 ...
JOSÉ Vanterler Costa Sousa +1 more
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A new definition of fractional derivative
Journal of Computational and Applied Mathematics, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Roshdi Khalil +3 more
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Generalization of Caputo-Fabrizio Fractional Derivative and Applications to Electrical Circuits
Frontiers in Physics, 2020 A new fractional derivative with a non-singular kernel involving exponential and trigonometric functions is proposed in this paper. The suggested fractional operator includes as a special case Caputo-Fabrizio fractional derivative.
Sunil Kumar +2 more
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A New Mixed Fractional Derivative with Applications in Computational Biology
ComputationThis study develops a new definition of a fractional derivative that mixes the definitions of fractional derivatives with singular and non-singular kernels.
Khalid Hattaf
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Journal of Function Spaces, 2020 In this paper, we made improvement on the conformable fractional derivative. Compared to the original one, the improved conformable fractional derivative can be a better replacement of the classical Riemann-Liouville and Caputo fractional derivative in ...
Feng Gao, Chunmei Chi
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On Hilfer generalized proportional fractional derivative
Advances in Difference Equations, 2020 Motivated by the Hilfer and the Hilfer–Katugampola fractional derivative, we introduce in this paper a new Hilfer generalized proportional fractional derivative, which unifies the Riemann–Liouville and Caputo generalized proportional fractional ...
Idris Ahmed +4 more
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Fractional Newton mechanics with conformable fractional derivative
Journal of Computational and Applied Mathematics, 2015 This paper studies fractional Newtonian mechanics with the tools of conformable fractional derivative and integral. This new fractional derivative is well-behaved and obeys the Leibniz and chain rules, an essential difference compared with the Riemann-Liouville and Caputo derivatives.
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