Lyapunov functions for fractional‐order nonlinear systems with Atangana–Baleanu derivative of Riemann–Liouville type
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DOI: 10.1002/mma.7690
Abstract: Stability analysis plays an essential role in control systems design. This analysis can be done using different techniques that show the equilibrium points are stable (or unstable). This paper focuses on fractional systems of order… read more here.
Keywords: baleanu derivative; atangana baleanu; derivative riemann; riemann liouville ... See more keywords
Fractional Elementary Bicomplex Functions in the Riemann–Liouville Sense
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DOI: 10.1007/s00006-021-01165-0
Abstract: In this paper, we present the development of fractional bicomplex calculus in the Riemann–Liouville sense, based on the modification of the Cauchy–Riemann operator using the one-dimensional Riemann–Liouville derivative in each direction of the bicomplex basis.… read more here.
Keywords: riemann liouville; bicomplex; liouville sense; fractional elementary ... See more keywords
Spectral collocation method for nonlinear Riemann–Liouville fractional differential system
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DOI: 10.1007/s10092-021-00403-y
Abstract: The spectral collocation method is investigated for the system of nonlinear Riemann–Liouville fractional differential equations (FDEs). The main idea of the presented method is to solve the corresponding system of nonlinear weakly singular Volterra integral… read more here.
Keywords: system; fractional differential; liouville fractional; riemann liouville ... See more keywords
Spectral Theorems Associated with the Riemann–Liouville Two-Wavelet Localization Operators
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DOI: 10.1007/s10476-018-0609-y
Abstract: In this paper, we prove the boundedness and compactness of localization operators associated with Riemann–Liouville wavelet transforms, which depend on a symbol and two Riemann–Liouville wavelets on Lp(dνα), 1 ≤ p ≤ ∞. read more here.
Keywords: localization operators; wavelet; associated riemann; spectral theorems ... See more keywords
Uncertainty principles for continuous wavelet transforms related to the Riemann–Liouville operator
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DOI: 10.1007/s11587-017-0320-5
Abstract: In this paper we define and study the continuous wavelet transforms associated with the Riemann–Liouville operator, we give nice harmonic analysis results. Next we establish an analogue of Heisenberg’s inequality related to the wavelet transform.… read more here.
Keywords: continuous wavelet; liouville operator; wavelet transforms; wavelet ... See more keywords
On the Hyers–Ulam stability of Riemann–Liouville multi-order fractional differential equations
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DOI: 10.1007/s13370-019-00701-3
Abstract: In this paper, by using a Bielecki’s type norm and Banach fixed point theorem, we obtain a result on the Hyers–Ulam stability of Riemann–Liouville multi-order fractional differential equations. read more here.
Keywords: hyers ulam; stability riemann; ulam stability; liouville multi ... See more keywords
On a $$\psi $$-Generalized Fractional Derivative Operator of Riemann–Liouville with Some Applications
Sign Up to like & getrecommendations! Published in 2020 at "International Journal of Applied and Computational Mathematics"
DOI: 10.1007/s40819-020-00892-5
Abstract: Various extended beta functions have been investigated by many researchers (Mubeen et al. in FJMS 102:1545–1557, 2017; Ozergin et al. in J Comput Appl Math 235:4601–4610, 2011; Parmar et al. in J Class Anal 11:91–106,… read more here.
Keywords: fractional derivative; riemann liouville; derivative operator; psi generalized ... See more keywords
Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties
Sign Up to like & getrecommendations! Published in 2018 at "Physica A: Statistical Mechanics and its Applications"
DOI: 10.1016/j.physa.2018.03.056
Abstract: Abstract We presented an analysis of evolutions equations generated by three fractional derivatives namely the Riemann–Liouville, Caputo–Fabrizio and the Atangana–Baleanu fractional derivatives. For each evolution equation, we presented the exact solution for time variable and… read more here.
Keywords: atangana baleanu; semigroup; time; semigroup principle ... See more keywords
The right Riemann–Liouville fractional Hermite–Hadamard type inequalities derived from Green’s function
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DOI: 10.1063/1.5143908
Abstract: The purpose of this work is to present the right Riemann–Liouville fractional integral version of Hermite–Hadamard inequality via a relatively new method through the Green’s function approach. In the process, some identities are established. Using… read more here.
Keywords: right riemann; green function; liouville fractional; riemann liouville ... See more keywords
Refinements of bullen-type inequalities for s–convex functions via Riemann-Liouville fractional integrals involving Gauss hypergeometric function
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Interdisciplinary Mathematics"
DOI: 10.1080/09720502.2019.1698803
Abstract: Abstract In this paper, the author establishes a new identity for differentiable functions and obtain some new inequalities for differentiable functions based on s–convexity via Riemann-Liouville fractional integrals involving Gauss hypergeometric function. read more here.
Keywords: integrals involving; involving gauss; fractional integrals; liouville fractional ... See more keywords
Synchronization for Incommensurate Riemann–Liouville Fractional-Order Time-Delayed Competitive Neural Networks With Different Time Scales and Known or Unknown Parameters1
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Computational and Nonlinear Dynamics"
DOI: 10.1115/1.4042494
Abstract: Synchronization for incommensurate Riemann–Liouville fractional competitive neural networks (CNN) with different time scales is investigated in this paper. Time delays and unknown parameters are concerned in the model, which is more practical. Two simple and… read more here.
Keywords: liouville fractional; incommensurate riemann; time; synchronization incommensurate ... See more keywords