Fractional physical problems including wind-influenced projectile motion with Mittag-Leffler kernel

Özarslan, Ramazan; Baş, Erdal; Băleanu, Dumitru; Acay, Bahar

doi:10.3934/math.2020031

Cited by 23 publications

(17 citation statements)

References 17 publications

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“…where α, ρ, and γ are arbitrary parameters, and the dimensionality of σ is the second (s). Hence, we employ this approach in order to get the solutions of the fractional electrical circuits with the help of the Caputo-type M-derivative [9,19,26].…”

Section: Fractional Electrical Circuitsmentioning

confidence: 99%

Electrical Circuits RC, LC, and RLC under Generalized Type Non-Local Singular Fractional Operator

Acay

Inc

2021

Fractal Fract

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The current study is of interest when performing a useful extension of a crucial physical problem through a non-local singular fractional operator. We provide solutions that include three arbitrary parameters α, ρ, and γ for the Resistance-Capacitance (RC), Inductance-Capacitance (LC), and Resistance-Inductance-Capacitance (RLC) electric circuits utilizing a generalized type fractional operator in the sense of Caputo, called non-local M-derivative. Additionally, to keep the dimensionality of the physical parameter in the proposed model, we use an auxiliary parameter. Owing to the fact that all solutions depend on three parameters unlike the other solutions containing one or two parameters in the literature, the solutions obtained in this study have more general results. On the other hand, in order to observe the advantages of the non-local M-derivative, a comprehensive comparison is carried out in the light of experimental data. We make this comparison for the RC circuit between the non-local M-derivative and Caputo derivative. It is clearly shown on graphs that the fractional M-derivative behaves closer to the experimental data thanks to the added parameters α, ρ, and γ.

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Section: Fractional Electrical Circuitsmentioning

confidence: 99%

Electrical Circuits RC, LC, and RLC under Generalized Type Non-Local Singular Fractional Operator

Acay

Inc

2021

Fractal Fract

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“…We can give the model (3) in fractional cases, ABC, CFC, and Caputo, under different higher orders, so one can find analytical solutions by using LT. Especially, we use Sontakke and Shaikh 53 and Ozarslan et al 54 for obtaining inverse LT of higher order ABC fractional modeling problems. 3.1.1 ABC fractional cases 1.…”

Section: Model Development In Fractional Casesmentioning

confidence: 99%

Microbial survival and growth modeling in frame of nonsingular fractional derivatives

Özarslan

2020

Math Methods in App Sciences

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In this article, the two‐parameter Weibull model (3) is considered for microbial survival curves by new fractional differential operators to analyze some microbial, common reasons of illnesses, and outbreaks, such as Salmonella spp. cocktail in ground turkey thigh, pork shoulder, and turkey breast at isothermal cooking conditions in 50°C, 54°C, 58°C, 62°C, and 66°C, then Listeria monocytogenes and Escherichia coli O157:H7 are considered in ground beef in the same thermal conditions. Results obtained with nonsingular fractional derivatives, including exponential decay and Mittag‐Leffler kernel, are analyzed comparatively with Caputo fractional and integer‐order derivatives for survival ratio of microbial cells. In the sequel, E. coli O157:H7 in ground beef, Salmonella typhimurium and S. enteritidis in boneless pork chops, and background flora in ground pork and at room temperature, 10°C, 7.2°C, and 4.4°C are considered for microbial growth curves by nonsingular fractional operators, and results obtained are compared with Caputo fractional and integer‐order derivatives. All results for advantage and disadvantage of Atangana‐Baleanu and Caputo‐Fabrizio fractional derivatives are discussed in detail.

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“…Fractional order calculus has a wide range of applications in a variety of areas due to its efficient properties, including biology and physics. [2][3][4], economics and finance [5,6], science and engineering [7,8], and mathematical modeling and mechanics [9][10][11]. Since the kernel of Caputo and Riemann derivatives is singular, they have a problem with this kernel.…”

Section: Introductionmentioning

confidence: 99%

A Novel Homotopy Perturbation Method with Applications to Nonlinear Fractional Order KdV and Burger Equation with Exponential-Decay Kernel

Ahmad

Ullah

Akgül

et al. 2021

Journal of Function Spaces

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In this paper, we introduce the Yang transform homotopy perturbation method (YTHPM), which is a novel method. We provide formulae for the Yang transform of Caputo-Fabrizio fractional order derivatives. We derive an algorithm for the solution of Caputo-Fabrizio (CF) fractional order partial differential equation in series form and show its convergence to the exact solution. To demonstrate the novel approach, we include some examples with detailed solutions. We use tables and graphs to compare the exact and approximate solutions.

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Fractional physical problems including wind-influenced projectile motion with Mittag-Leffler kernel

Cited by 23 publications

References 17 publications

Electrical Circuits RC, LC, and RLC under Generalized Type Non-Local Singular Fractional Operator

Electrical Circuits RC, LC, and RLC under Generalized Type Non-Local Singular Fractional Operator

Microbial survival and growth modeling in frame of nonsingular fractional derivatives

A Novel Homotopy Perturbation Method with Applications to Nonlinear Fractional Order KdV and Burger Equation with Exponential-Decay Kernel

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