Principal resonance analysis of piecewise nonlinear oscillator with fractional calculus

Article Engineering, Electrical & Electronic

Fractional Fourier Transform based Riesz fractional derivative approach for edge detection and its application in image enhancement

Kanwarpreet Kaur et al.

Summary: This paper proposes an edge detection technique based on Riesz fractional derivative in the Fractional Fourier Transform domain, which is validated through various performance metrics and further validation.

SIGNAL PROCESSING (2021)

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Article Mathematics, Applied

A numerical method for two-dimensional multi-term time-space fractional nonlinear diffusion-wave equations

Jianfei Huang et al.

Summary: This paper presents an efficient alternating direction implicit (ADI) scheme for two-dimensional multi-term time-space fractional nonlinear diffusion-wave equations, which transforms the problem equivalently, constructs the scheme, and discusses fast implementation techniques to establish solvability, unconditional stability, and convergence of the proposed ADI scheme.

APPLIED NUMERICAL MATHEMATICS (2021)

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Article Mathematics, Interdisciplinary Applications

A discussion on the approximate controllability of Hilfer fractional neutral stochastic integro-differential systems

C. Dineshkumar et al.

Summary: This manuscript focuses on the approximate controllability of Hilfer fractional neutral stochastic integro-differential equations, proving the principal results based on theoretical concepts related to fractional calculus and Schauder's fixed-point theorem. It discusses the approximate controllability of the fractional evolution system and extends the results to nonlocal conditions. Theoretical and practical applications are provided to enhance the effectiveness of the discussion.

CHAOS SOLITONS & FRACTALS (2021)

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Article Mathematics, Interdisciplinary Applications

Results on approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type

K. Kavitha et al.

Summary: This research paper focuses on the approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type. By combining fractional calculus techniques, fixed point theorem for multi-value dmaps, and Sobolev-type and Clarke subdifferential, new existence results of mild solutions are obtained. Linear and semilinear systems for approximate controllability are demonstrated, and an illustration is included to verify the theoretical results.

CHAOS SOLITONS & FRACTALS (2021)

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Article Mathematics, Applied

New discussion on approximate controllability results for fractional Sobolev type Volterra-Fredholm integro-differential systems of order 1 < r < 2

V. Vijayakumar et al.

Summary: The article focuses on approximate controllability results for fractional Sobolev type Volterra-Fredholm integro-differential inclusions with order 1 < r < 2. By utilizing ideas related to cosine function of operators, fractional calculus, and fixed point approach, the main results are established, with further examination of the system using the concept of nonlocal conditions, and an example provided to demonstrate the theory.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS (2021)

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Article Computer Science, Interdisciplinary Applications

A note on the approximate controllability of Sobolev type fractional stochastic integro-differential delay inclusions with order 1 < r < 2

C. Dineshkumar et al.

Summary: This paper mainly focuses on the approximate controllability of Sobolev type fractional stochastic integrodifferential delay inclusions with order 1 < r < 2, the primary outcomes are proved using results associated with fractional calculus, multivalued maps, and the Bohnenblust and Karlin's fixed point theorem. The discussion starts with approximate controllability and then extends to systems with nonlocal conditions, and concludes by providing an application to illustrate the obtained theoretical results.

MATHEMATICS AND COMPUTERS IN SIMULATION (2021)

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Article Mathematics, Applied

An analysis of a mathematical fractional model of hybrid viscous nanofluids and its application in heat and mass transfer

Rizwan Ali et al.

Summary: This study investigates the modeling of heat and mass transfer flow of hybrid nanofluid in water and engine oil, utilizing Caputo fractional power law derivative and Laplace transform technique. The results show that variations in fractional parameters alpha, beta, and gamma can control the behavior of the fluid, with water-based hybrid nanofluids having higher temperature and velocity compared to engine oil-based ones. Comparisons with previous results indicate good agreement in limiting cases.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2021)

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Article Mathematics, Applied

Stability analysis of multi-term fractional-differential equations with three fractional derivatives

Oana Brandibur et al.

Summary: This study presents necessary and sufficient stability and instability conditions for multi-term homogeneous linear fractional differential equations with three Caputo derivatives and constant coefficients. The results provide fractional-order-dependent as well as fractional-order-independent characterisations of stability and instability properties in terms of the coefficients of the equations. Specific cases including Basset and Bagley-Torvik equations are exemplified, along with a multi-term fractional differential equation of an inextensible pendulum with fractional damping terms, and a fractional harmonic oscillator.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2021)

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Article Engineering, Mechanical

Smart dampers-based vibration control - Part 2: Fractional-order sliding control for vehicle suspension system

Sy Dzung Nguyen et al.

Summary: Semi-active suspension systems using smart dampers like magnetorheological dampers are being developed to improve ride comfort and road holding of vehicles. A new control system based on fractional-order derivatives is proposed for the half-car semi-active suspension system with MRDs. The control system consists of I-SmDs and FD-based sliding mode control technique, which determines control force and estimates current intensity applied to MRDs. Studies are conducted to verify the control effectiveness and development potential of this method.

MECHANICAL SYSTEMS AND SIGNAL PROCESSING (2021)

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Article Mathematics, Applied

Hyperchaotic behaviors, optimal control, and synchronization of a nonautonomous cardiac conduction system

Dumitru Baleanu et al.

Summary: This paper investigates the hyperchaos analysis, optimal control, and synchronization of a nonautonomous cardiac conduction system. Various approaches are used to analyze, control, and synchronize the hyperchaotic behaviors, demonstrating the efficacy of proposed strategies through simulation and theoretical justification. The new nonlinear fractional model shows more flexible behavior than its classical counterpart due to its memory effects.

ADVANCES IN DIFFERENCE EQUATIONS (2021)

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Article Automation & Control Systems

Modeling and Control of Piezoelectric Hysteresis: A Polynomial-Based Fractional Order Disturbance Compensation Approach

Chen Yang et al.

Summary: Piezoelectric hysteresis is a critical issue affecting the motion accuracy of piezo-actuated nanopositioners, and this article proposes a novel method based on a polynomial-based fractional order disturbance model to address this challenge. The method does not require expensive computational resources and can be easily implemented in an analog manner, offering advantages of high bandwidth and low cost. Extensive modeling and tracking experiments demonstrate the effectiveness of the proposed method in significantly suppressing piezoelectric hysteresis nonlinearity over a wide bandwidth.

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS (2021)

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Article Mathematics, Applied

On a nonlinear dynamical system with both chaotic and nonchaotic behaviors: a new fractional analysis and control

Dumitru Baleanu et al.

Summary: This paper analyzes the dynamic motion of a quarter-car suspension system with sinusoidal road excitation force, introducing a new fractional-order differential equations mathematical model and proposing a quadratic numerical method to solve the related equations. By investigating time-domain responses and phase portraits, both chaotic and non-chaotic behaviors of the system can be identified through the fractional-order model. A state-feedback controller and chaos optimal control are presented to overcome chaotic oscillations in the system, with simulation results demonstrating the effectiveness of the proposed modeling and control strategies.

ADVANCES IN DIFFERENCE EQUATIONS (2021)

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Article Mathematics, Applied

Results concerning to approximate controllability of non-densely defined Sobolev-type Hilfer fractional neutral delay differential system

Kottakkaran Sooppy Nisar et al.

Summary: This manuscript focuses on the approximate controllability outcomes for non-densely defined Sobolev-type Hilfer fractional neutral differential system with infinite delay, using findings in fractional theory and the fixed-point method. The discussion primarily covers existence and approximate controllability, with an example provided for demonstration of the theory.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2021)

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Article Mathematics, Applied

A nonstandard finite difference scheme for the modeling and nonidentical synchronization of a novel fractional chaotic system

Dumitru Baleanu et al.

Summary: This paper introduces and analyzes a novel fractional chaotic system with quadratic and cubic nonlinearities. Numerical simulations determine the lowest order at which the system remains chaotic, and the system's chaotic behavior is studied using a nonstandard finite difference scheme. Additionally, nonidentical synchronization between the model and fractional Volta equations is achieved through an active control strategy, confirming its effectiveness through simulations.

ADVANCES IN DIFFERENCE EQUATIONS (2021)

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Article Engineering, Mechanical