Similarity Analytic Solutions of a 3D-Fractal Nanofluid Uncoupled System Optimized by a Fractal Symmetric Tangent Function

Ibrahim, Rabha W.; Ajaj, Ahmed M.; Al-Saidi, Nadia M. G.; Balean, Dumitru

doi:10.32604/cmes.2022.018348

Cited by 5 publications

(3 citation statements)

References 23 publications

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“…The quantum and fractional calculus are the most extensively used in image enhancement methods [6]. Quantum calculus (q-calculus) is a relatively recent field of mathematics that allows the fractional derivative of a real function to be calculated without bounds [7,8]. Several image enhancing approaches with various mathematical models have been developed in the literature.…”

Section: Introductionmentioning

confidence: 99%

Pixel’s Quantum Image Enhancement Using Quantum Calculus

Abdul-Wahed¹,

Băleanu²,

Ibrahim³

et al. 2023

CMC

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The current study provides a quantum calculus-based medical image enhancement technique that dynamically chooses the spatial distribution of image pixel intensity values. The technique focuses on boosting the edges and texture of an image while leaving the smooth areas alone. The brain Magnetic Resonance Imaging (MRI) scans are used to visualize the tumors that have spread throughout the brain in order to gain a better understanding of the stage of brain cancer. Accurately detecting brain cancer is a complex challenge that the medical system faces when diagnosing the disease. To solve this issue, this research offers a quantum calculus-based MRI image enhancement as a pre-processing step for brain cancer diagnosis. The proposed image enhancement approach improves images with low gray level changes by estimating the pixel's quantum probability. The suggested image enhancement technique is demonstrated to be robust and resistant to major quality changes on a variety of MRI scan datasets of variable quality. For MRI scans, the BRISQUE "blind/referenceless image spatial quality evaluator" and the NIQE "natural image quality evaluator" measures were 39.38 and 3.58, respectively. The proposed image enhancement model, according to the data, produces the best image quality ratings, and it may be able to aid medical experts in the diagnosis process. The experimental results were achieved using a publicly available collection of MRI scans.

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Section: Introductionmentioning

confidence: 99%

Pixel’s Quantum Image Enhancement Using Quantum Calculus

Abdul-Wahed¹,

Băleanu²,

Ibrahim³

et al. 2023

CMC

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“…The numerical methods required the linearization and discretization procedure and these procedures sometimes affect the accuracy of the methods that is why the scientists used the analytical method to solve the nonlinear fractional PDEs. The applications of these methods can be seen in [41][42][43][44][45][46][47][48][49][50][51][52][53].…”

Section: Introductionmentioning

confidence: 99%

Modifications of the Optimal Auxiliary Function Method to Fractional Order Fornberg-Whitham Equations

Ullah¹,

Fiza²,

Khan³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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In this paper, we present a new modification of the newly developed semi-analytical method named the Optimal Auxilary Function Method (OAFM) for fractional-order equations using the Caputo operator, which is named FOAFM. The mathematical theory of FOAFM is presented and the effectiveness of this method is proven by using it with well-known Fornberg-Whitham Equations (FWE). The FOAFM results are compared with other method results along with their exact solutions with the help of tables and plots to prove the validity of FOAFM. A rapidly convergent series solution is obtained from FOAFM and is validated by comparison with other results. The analysis proves that our method is simply applicable, contains less computational work, and is rapidly convergent to the exact solution at the first iteration. A series solution to the problem is obtained with the help of FOAFM. The validity of FOAFM results is validated by comparing its results with the results available in the literature. It is observed that FOAFM is simply applicable, contains less computational work, and is fastly convergent. The convergence and stability are obtained with the help of optimal constants. FOAFM is very easy in applicability and provides excellent results at the first iteration for complex nonlinear initial/boundary value problems. FOAFM contains the optimal auxiliary constants through which we can control the convergence as FOAFM contains the auxiliary functions D 1 , D 2 , D 3 . . . in which the optimal constants G 1 , G 2 , . . . and the control convergence parameters exist to play an important role in getting the convergent solution which is obtained rigorously. The computational work in FOAFM is less when compared to other methods and even a low-specification computer can do the computational work easily.

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“…Furthermore, conservative chaotic mapping has been revealed in [23,24]. Hidden chaotic attractors and hidden periodic oscillations have been investigated in drilling systems [25], phase-locked loops, and in aviation control system [26,27]. The attraction basin for hidden attractor's is not connected to any nearby regions of equilibrium, which shows that these attractors are different from self-excited attractors.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Hidden Attractors in Four-Dimensional Dynamical Systems with Power Law

Khan

Saifullah

et al. 2022

Journal of Function Spaces

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Four-dimensional continuous chaotic models with Caputo fractional derivative are presented. Fixed point theory is used to investigate the existence and uniqueness of complex systems. The dynamical properties are studied, including the Lyapunov exponent, phase portrait, and time series analysis. The hyperchaotic nature of each system is revealed by the positive exponents. The numerical method is introduced to describe the influence of the order of the Caputo fractional derivative. The phase portraits are presented to investigate the behavior and effect of some key parameters and fractional orders on model dynamics. The systems approach fixed point attractors for fractional-order and increase the visibility of the attractor by decreasing fractional order. This means that a change in fractional order has a significant impact on the dynamics of the models. When the order of the derivative is equal to one, both systems oscillate frequently. However, as the fractional order is reduced, the system oscillations decrease as compared to the integer-order, and the system moves towards its fixed point, reveals the hidden attractors inherent in the system, and enabling it to develop to a stable state more efficiently.

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Similarity Analytic Solutions of a 3D-Fractal Nanofluid Uncoupled System Optimized by a Fractal Symmetric Tangent Function

Cited by 5 publications

References 23 publications

Pixel’s Quantum Image Enhancement Using Quantum Calculus

Pixel’s Quantum Image Enhancement Using Quantum Calculus

Modifications of the Optimal Auxiliary Function Method to Fractional Order Fornberg-Whitham Equations

Dynamics of Hidden Attractors in Four-Dimensional Dynamical Systems with Power Law

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