Analysis of projectile motion in view of conformable derivative

Contreras, Abraham Ortega; Rosales, J. J.; Jiménez, Leonardo Martínez; Cruz–Duarte, Jorge M.

doi:10.1515/phys-2018-0076

Cited by 12 publications

(3 citation statements)

References 18 publications

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“…(Zhao and kang Luo 2017) proposed the physical interpretation and application of the general conformable fractional derivative. Many applications of fractional derivatives and fractional integrals are discussed by (Butera and Paola 2014;Contreras et al 2018;Cresson 2010;Zhao and kang Luo 2017;Zhou et al 2018), and the analytic solution of the time-fractional heat equation is also pointed out, which may be further resorted to in (Hammad and Khalil 2014a,b).…”

Section: Chaosmentioning

confidence: 99%

A New Fractional-order Derivative-based Nonlinear Anisotropic Diffusion Model for Biomedical Imaging

CHAUHAN,

KUMAR,

KARACA

2023

Chaos Theory and Applications

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Nonlinear anisotropic diffusion equations are employed to ensure the improvement of the image quality by removing noise while retaining the subtle details and edges. Image denoising is observed to be of utmost importance in image processing and computer vision to prepare the images with better resolutions. Partial differential equations (PDEs), in this sense, can be used extensively in different aspects with regard to image processing ranging from filtering to restoration, segmentation to edge enhancement and detection, denoising in particular, among the other ones. The medical images (ultrasound images, X-rays, CT scans, MRIs, etc.) may lose significant features and become degraded due to the emergence of noise. As a result, the process of improvement pertaining to medical images has become a thought-provoking area of inquiry with challenges related to detecting the additive noise in the images and finding the applicable solution in a timely manner. To this end, numerous denoising techniques have been established. In this research paper, we present a conformable fractional derivative-based anisotropic diffusion model for removing speckle noise in ultrasound images. Chaos, as a ubiquitous phenomenon in nature, manifests the fact that the observed chaotic and noisy signals are often disrupted by external interferences. Edge, as one of the most remarkable features for images, requires denoising via nonlinear means to attain optimal outcomes. The finite difference method is used to discretize the fractional diffusion model and classical diffusion models. The peak signal-to-noise ratio (PSNR) is used for the quality of the smooth images. The aim of this study is to prove the viscosity solution of the diffusion model with the proposed model providing to be efficient in reducing noise by preserving the essential image features like edges, corners and other sharp structures for ultrasound images in comparison to the classical anisotropic diffusion model. Comparative experimental results corroborate that the proposed and extended mathematical model is capable of denoising and preserving the significant features in ultrasound within the framework of biomedical imaging and other related medical, clinical and image-signal related applied as well as computational processes.

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Section: Chaosmentioning

confidence: 99%

A New Fractional-order Derivative-based Nonlinear Anisotropic Diffusion Model for Biomedical Imaging

CHAUHAN,

KUMAR,

KARACA

2023

Chaos Theory and Applications

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“…The under the influence of environmental effects the projectile trajectories are nurturedin [37] by the aid of mathematical models and derived some stimulating consequences with respect to sniper rifle, Magnus effect and degree of freedom ballistic models. On another side many numerical schemes are employed by researchers to investigate about the projected models including the projectile motion is analysed by the fractional approach in [38], projectile motion with two dimensions is studied in [39], this phenomenon with a resisting medium [40], and many others [41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Fractional approach for analysis of the model describing wind-influenced projectile motion

2021

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In this paper, we find the solution for coupled equations describing the projectile motion with wind-influence using q -homotopy analysis transform method ( q -HATM). The projectedmethod is elegant amalgamations of q -homotopy analysis scheme and Laplace transform, and fractional derivativedefined withCaputo-Fabrizio (CF) operator. Moreover, the physical natures of the obtained results have been captured in terms of plots for diverse mass, external force and fractional order. The achievedconsequences elucidate that, the hiredsolution procedure is easy to implement, highly methodical as well as accurate to analyse the behaviour of system of nonlinear differential equations of both integer and fractional order describing connected areas of science and engineering.

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“…Two-dimensional projectile motion in a free and in a resistive medium were investigated using the so-called conformable derivative in Ref. [39]. The motion of a projectile by using the Riemann-Liouville fractional derivative and the Caputo approach is studied in Refs.…”

Section: Introductionmentioning

confidence: 99%

The investigation of classical particle in the presence of fractional calculus

Chung¹,

Zare²,

Hassanabadi³

et al. 2020

Rev. Mex. Fís.

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In this article, by applying a preliminary and comprehensive definition of the fractional calculus, the effect of this calculus on the fractional derivatives corresponding to different aspects of physics such as Laplace transforms, Riemann-Liouville and Caputo has been specified. Applications of the fractional calculus in studying the dynamics of particle motion in classical mechanics are investigated analytically. Furthermore, we compare our results with those given in the ordinary condition and we show that this condition is simply found by removing the fractional effects and the expected results are obtained.

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Analysis of projectile motion in view of conformable derivative

Cited by 12 publications

References 18 publications

A New Fractional-order Derivative-based Nonlinear Anisotropic Diffusion Model for Biomedical Imaging

A New Fractional-order Derivative-based Nonlinear Anisotropic Diffusion Model for Biomedical Imaging

Fractional approach for analysis of the model describing wind-influenced projectile motion

The investigation of classical particle in the presence of fractional calculus

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