Non Integer Order Operators Implementation via Switched Capacitors Technology

Continuous orthogonal moments, for which continuous functions are used as kernel functions, are invariant to rotation and scaling, and they have been greatly developed over the recent years. Among continuous orthogonal moments, polar harmonic Fourier moments (PHFMs) have superior performance and strong image description ability. In order to improve the performance of PHFMs in noise resistance and image reconstruction, PHFMs, which can only take integer numbers, are extended to fractional-order polar harmonic Fourier moments (FrPHFMs) in this paper. Firstly, the radial polynomials of integer-order PHFMs are modified to obtain fractional-order radial polynomials, and FrPHFMs are constructed based on the fractional-order radial polynomials; subsequently, the strong reconstruction ability, orthogonality, and geometric invariance of the proposed FrPHFMs are proven; and, finally, the performance of the proposed FrPHFMs is compared with that of integer-order PHFMs, fractional-order radial harmonic Fourier moments (FrRHFMs), fractional-order polar harmonic transforms (FrPHTs), and fractional-order Zernike moments (FrZMs). The experimental results show that the FrPHFMs constructed in this paper are superior to integer-order PHFMs and other fractional-order continuous orthogonal moments in terms of performance in image reconstruction and object recognition, as well as that the proposed FrPHFMs have strong image description ability and good stability.

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Dynamical study of non-integer order predator–prey system with fear effect

International Journal of Modelling and Simulation ◽

10.1080/02286203.2021.1926049 ◽

2021 ◽

pp. 1-9

Author(s):

Debasis Mukherjee

Keyword(s):

Dynamical Study ◽

Predator Prey ◽

Integer Order ◽

Fear Effect ◽

Prey System

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Switched capacitors: a bridge between analog and digital SP

2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03). ◽

10.1109/icassp.2003.1199584 ◽

2003 ◽

Cited By ~ 2

Author(s):

R. Saint-Nom ◽

D. Jacoby

Keyword(s):

Switched Capacitors

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New Challenges Arising in Engineering Problems with Fractional and Integer Order

Fractal and Fractional ◽

10.3390/fractalfract5020035 ◽

2021 ◽

Vol 5 (2) ◽

pp. 35

Author(s):

Haci Mehmet Baskonus ◽

Luis Manuel Sánchez Ruiz ◽

Armando Ciancio

Keyword(s):

Mathematical Models ◽

Real World ◽

Integer Order ◽

Engineering Problems ◽

New Challenges ◽

Real World Problems

Mathematical models have been frequently studied in recent decades in order to obtain the deeper properties of real-world problems [...]

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Analysis of a New Class of Impulsive Implicit Sequential Fractional Differential Equations

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2019-0030 ◽

2020 ◽

Vol 21 (6) ◽

pp. 571-587 ◽

Cited By ~ 2

Author(s):

Akbar Zada ◽

Sartaj Ali ◽

Tongxing Li

Keyword(s):

Differential Equations ◽

Fractional Order ◽

Fractional Differential Equations ◽

Sufficient Conditions ◽

Uniqueness Of Solutions ◽

Integer Order ◽

New Class ◽

Proposed Model ◽

Fractional Differential ◽

Sequential Fractional Differential Equations

AbstractIn this paper, we study an implicit sequential fractional order differential equation with non-instantaneous impulses and multi-point boundary conditions. The article comprehensively elaborate four different types of Ulam’s stability in the lights of generalized Diaz Margolis’s fixed point theorem. Moreover, some sufficient conditions are constructed to observe the existence and uniqueness of solutions for the proposed model. The proposed model contains both the integer order and fractional order derivatives. Thus, the exponential function appearers in the solution of the proposed model which will lead researchers to study fractional differential equations with well known methods of integer order differential equations. In the last, few examples are provided to show the applicability of our main results.

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