Discrete fractional solutions to the k‐hypergeometric differential equation
Sign Up to like & getrecommendations! Published in 2020 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.6460
Abstract: In this study, the discrete fractional nabla calculus operator is used to investigate the k‐hypergeometric differential equation for both homogeneous and nonhomogeneous states. To solve the guiding equation, we implement certain classical transformations and also… read more here.
Keywords: discrete fractional; fractional solutions; solutions hypergeometric; differential equation ... See more keywords
A Low-Complexity Approach to Computation of the Discrete Fractional Fourier Transform
Sign Up to like & getrecommendations! Published in 2017 at "Circuits, Systems, and Signal Processing"
DOI: 10.1007/s00034-017-0503-z
Abstract: This paper proposes an effective approach to the computation of the discrete fractional Fourier transform for an input vector of any length N. This approach uses specific structural properties of the discrete fractional Fourier transformation… read more here.
Keywords: computation; discrete fractional; fractional fourier; approach ... See more keywords
Synchronization of discrete fractional-order complex networks with and without unknown topology.
Sign Up to like & getrecommendations! Published in 2022 at "Chaos"
DOI: 10.1063/5.0072207
Abstract: This paper studies the outer synchronization problem of discrete fractional complex networks (DFCNs) with and without the presence of unknown topology. A discrete complex network with a fractional difference is first established and analyzed. By… read more here.
Keywords: topology; complex networks; unknown topology; discrete fractional ... See more keywords
Discrete fractional order PID controller design for nonlinear systems
Sign Up to like & getrecommendations! Published in 2021 at "International Journal of Systems Science"
DOI: 10.1080/00207721.2021.1924307
Abstract: ABSTRACT In this study, a discrete fractional order PID controller for nonlinear systems is proposed. U-model is firstly employed to transform nonlinear systems into a linear-like model and model complexity is then degraded and easier… read more here.
Keywords: fractional order; discrete fractional; controller; nonlinear systems ... See more keywords
Stability analysis and stabilisation of continuous-discrete fractional-order 2D Fornasini–Marchesini first model
Sign Up to like & getrecommendations! Published in 2022 at "International Journal of Systems Science"
DOI: 10.1080/00207721.2022.2122901
Abstract: This paper focuses on the structural stability and stabilisation of the continuous-discrete fractional-order two-dimensional Fornasini-Marchesini first model. The sufficient and necessary stability conditions are given in polynomial form at first. Secondly, to make the problem… read more here.
Keywords: stabilisation; discrete fractional; continuous discrete; stability ... See more keywords
On the dynamics of a Caputo-like discrete fractional Rössler system: chaos, stabilization and synchronization
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DOI: 10.1088/1402-4896/ac518f
Abstract: This study examines the dynamics of a novel Caputo-like discrete fractional Rössler system. The dynamics of this discrete fractional system are numerically analyzed using phase portraits, bifurcation diagrams and Lyapunov exponents. The study confirmed the… read more here.
Keywords: like discrete; system; fractional ssler; caputo like ... See more keywords
LMI-Based Stability Analysis of Continuous-Discrete Fractional-Order 2D Roesser Model
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Circuits and Systems II: Express Briefs"
DOI: 10.1109/tcsii.2021.3131183
Abstract: The manuscript investigates the problem of structural stability of continuous-discrete fractional-order 2D Roesser model. This model includes one continuous fractional-order dimension with fractional-order $\alpha \in (0,2)$ and one discrete dimension. By the equivalent transform and… read more here.
Keywords: discrete fractional; continuous discrete; model; stability ... See more keywords
On Hyers–Ulam Mittag-Leffler stability of discrete fractional Duffing equation with application on inverted pendulum
Sign Up to like & getrecommendations! Published in 2020 at "Advances in Difference Equations"
DOI: 10.1186/s13662-020-02920-6
Abstract: A human being standing upright with his feet as the pivot is the most popular example of the stabilized inverted pendulum. Achieving stability of the inverted pendulum has become common challenge for engineers. In this… read more here.
Keywords: discrete fractional; inverted pendulum; duffing equation; hyers ulam ... See more keywords
On nabla discrete fractional calculus operator for a modified Bessel equation
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DOI: 10.2298/tsci170614287y
Abstract: In thermal sciences, it is possible to encounter topics such as Bessel beams, Bessel functions or Bessel equations. In this work, we also present new discrete fractional solutions of the modified Bessel differential equation by… read more here.
Keywords: modified bessel; discrete fractional; fractional calculus; calculus operator ... See more keywords
Discrete fractional solution of a nonhomogeneous non-Fuchsian differential equations
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DOI: 10.2298/tsci180917336y
Abstract: In this article, we also present new fractional solutions of the non-homogeneous and homogeneous non-Fuchsian differential equation by using nabla-discrete fractional calculus operator ??(0 < ? < 1). So, we acquire new solution of these… read more here.
Keywords: fuchsian differential; discrete fractional; fractional solution; non fuchsian ... See more keywords
On Discrete Fractional Solutions of Non-Fuchsian Differential Equations
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DOI: 10.3390/math6120308
Abstract: In this article, we obtain new fractional solutions of the general class of non-Fuchsian differential equations by using discrete fractional nabla operator ∇ η ( 0 < η < 1 ) . This operator is… read more here.
Keywords: non fuchsian; discrete fractional; fractional solutions; differential equations ... See more keywords