Nonlinear Behavior in Fractional-Order Romeo and Juliet’s Love Model Influenced by External Force with Fuzzy Function

In this paper, a novel technique is proposed to solve fuzzy fractional delay differential equations (FFDDEs) with initial condition and source function, which are fuzzy triangular functions. The obtained solution is a fuzzy set of real functions. Each real function satisfies an FFDDE with a specific membership degree. A detailed algorithm is provided to solve the FFDDE. The proposed method has been elucidated in detail through numerical illustrations. Graphs are plotted using MATLAB.

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“…Step 4: We find solutions y u (χ) and y v (χ) to Eqs. (15) and (16), respectively. Then, the solution of Eq.…”

Section: Algorithm For the Solutionmentioning

confidence: 99%

“…Huang et al [14] analyzed the behavior of a chaotic system of a fractional order love model with an external environment. Moreover, Huang et al [15] studied the relationship of Romeo and Juliet love fractional model using a fuzzy function.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solutions of Fuzzy Fractional Delay Differential Equations

Padmapriya¹,

Kaliyappan²,

Manivannan³

2020

IJFIS

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“…Roohi et al [8] introduced fractional-order switching sliding surfaces into chaotic systems. Mandelbrot pointed out the existence of a large number of fractal dimensions in nature in 1983 [9], and fractional calculus has regained the attention of the profession in the social sciences [10,11] (such as love affairs, happiness, and family relationships) and in engineering [12] (such as electric engineering, electrical and communications engineering).The dynamics of fractional order systems are more complex and their fractional order derivatives have memory effects, which means that the current state of the system is not only affected by the initial conditions and current inputs, but also by the past inputs and past time states. This makes fractional order chaotic systems very important in some practical systems, such as stock price prediction, earthquake prediction, etc [13,14].…”

Section: Introductionmentioning

confidence: 99%

Finite-time synchronization of fractional-order chaotic system based on hidden attractors

Yan,

Zhang,

Jiang

et al. 2023

Phys. Scr.

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A new 3D fractional-order chaotic system is obtained by improving the Sprott-A system and introducing the definition of fractional calculus to it. Then the new system is certified to be chaotic by studying and analyzing the phase diagram, Lyapunov exponents, and smaller alignment index tests. Then the analysis of equilibrium points finds that the new system has virtually no equilibrium points and hidden attractors. The new system is dynamically analyzed by bifurcation diagram, time-domain waveform and complexity, it is indicated that the system is susceptible to initial conditions, and with the changes of different parameters the system produced different scroll types of attractors. In addition, to verify the feasibility of the system, a simulation circuit design based on Multisim is therefore carried out. Finally, the finite-time synchronization of the fractional-order system is successfully achieved by taking advantage of the high security of the hidden attractors.

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“…In this line, Atici and Eloe [7] developed nabla fractional Riemann-Liouville difference operator, initiated the study of nabla fractional initial value problem and established exponential law, product rule, and nabla Laplace transform. Following their works, the contributions of several mathematicians have made the theory of discrete fractional calculus a fruitful field of research in science and engineering, we refer here a few applications of discrete fractional equations [8][9][10]. We also refer here to a recent monograph by Goodrich and Peterson [11] and the references therein, which is an excellent source for all those who wish to work in this field.…”

Section: Introductionmentioning

confidence: 99%

Existence and Uniqueness of Solutions to a Nabla Fractional Difference Equation with Dual Nonlocal Boundary Conditions

Gopal

Jonnalagadda

2022

Foundations

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In this paper, we look at the two-point boundary value problem for a finite nabla fractional difference equation with dual non-local boundary conditions. First, we derive the associated Green’s function and some of its properties. Using the Guo–Krasnoselkii fixed point theorem on a suitable cone and under appropriate conditions on the non-linear part of the difference equation, we establish sufficient requirements for at least one and at least two positive solutions of the boundary value problem. Next, we discuss the existence and uniqueness of solutions to the considered problem. For this purpose, we use Brouwer and Banach fixed point theorem, respectively. Finally, we provide a few examples to illustrate the applicability of established results.

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Nonlinear Behavior in Fractional-Order Romeo and Juliet’s Love Model Influenced by External Force with Fuzzy Function

Cited by 19 publications

References 26 publications

Numerical Solutions of Fuzzy Fractional Delay Differential Equations

Numerical Solutions of Fuzzy Fractional Delay Differential Equations

Finite-time synchronization of fractional-order chaotic system based on hidden attractors

Existence and Uniqueness of Solutions to a Nabla Fractional Difference Equation with Dual Nonlocal Boundary Conditions

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