Dynamics of chaotic system based on image encryption through fractal-fractional operator of non-local kernel

Khan, Naveed; Ahmad, Zubair; Ahmad, Harith; Tchier, Fairouz; Zhang, Xiao-Zhong; Murtaza, Saqib

doi:10.1063/5.0085960

Cited by 18 publications

(7 citation statements)

References 25 publications

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“…After replacing the time fractional operator of FFD, Equations ( 7), (8), and (9) will transformed to:…”

Section: Fractal-fractional Modelmentioning

confidence: 99%

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Fractal‐fractional analysis and numerical simulation for the heat transfer of ZnO + Al₂O₃ + TiO₂/DW based ternary hybrid nanofluid

Murtaza,

Kumam,

Sutthibutpong

et al. 2023

Z Angew Math Mech

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Nanofluids are used to achieve maximum thermal performance with the smallest concentration of nanoparticles and stable suspension in conventional fluids. The effectiveness of nanofluids in convection processes is significantly influenced by their increased thermophysical characteristics. However, this technology is not ended here; binary and ternary nanofluids are now used to improve the efficiency of regular fluids. Therefore, this paper aims to analyze the natural convection Newtonian ternary nanofluid flow in a vertical channel. The tri‐hybridized nanoparticles of zinc oxide ZnO, Aluminum oxide Al2O3, and titanium oxide TiO2 is dissolved in base fluid distilled water (DW) to form a homogenous suspension. The impact of thermal radiation, joule heating, and viscous dissipation are also assumed. The classical Newtonian ternary nanofluid model has been generalized by using fractal‐fractional derivative (FFD) operator. The generalized model has been discretized by using the Crank–Nicolson scheme and then solved by using computational software. To analyze the behavior of fluid flow and heat distribution in fluid, the obtained solution was computed numerically and then plotted in response to different physical parameters. It is noted from the figure that when the volume fraction ϕ reaches to 0.04 (4% of the base fluid), the ternary nanofluid flow shows a significant amount of enhancement in heat transfer rate as compared to binary and unary nanofluid flows. This enhancement in the rate of heat transfer leads to improve the thermophysical characteristics such as viscosity, thermal expansion, and heat capacity etc. of the base fluid. It is also worth mentioning here that the thermal field is also enhance with the higher values of Eckert number , radiation parameter , and joule heating parameter .

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“…After replacing the time fractional operator of FFD, Equations ( 7), (8), and (9) will transformed to:…”

Section: Fractal-fractional Modelmentioning

confidence: 99%

“…The authors concluded that, fractal dimension provide larger memory effects than the usual fractional derivative. Similar articles on the applications of fractal‐fractional theory can be found in [5–10].…”

Section: Introductionmentioning

confidence: 98%

Fractal‐fractional analysis and numerical simulation for the heat transfer of ZnO + Al₂O₃ + TiO₂/DW based ternary hybrid nanofluid

Murtaza,

Kumam,

Sutthibutpong

et al. 2023

Z Angew Math Mech

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“…In additions, the said area have been used increasingly to investigate various viral infectious diseases including Hepatitis B, and others in [12,13,28,29]. Moreover some interesting applicable in fluid mechanics, vegetable oil process, electromagnetic theory, pine wilt disease can be read in the cited articles as [1,16,[22][23][24].…”

Section: Introductionmentioning

confidence: 99%

On boundary values system of sequential hybrid fractional differential equations

Shah,

Gul,

Khan

et al. 2024

J. Math. Computer Sci.

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This work is devoted to study a broad system of sequential hybrid fractional differential equations (S-HFDEs). Sufficient conditions related to the existence theory for the aforementioned system are investigated by utilizing the coincidence degree theory of topology. The mentioned degree theory is a powerful instrument which can be utilized to examine a wide range of nonlinear problems for qualitative theory. In addition, for the system of boundary value problems (BVPs) of S-HFDEs under consideration, a result concerning the Ullam-Hyers (U-H) stability is also developed. A pertinent example is also given to verify our theoretical results.

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“…Since the advent of integer derivatives, research on fractional-order derivatives has been conducted. This idea has gained a lot of acceptance over the past three decades 40 – 44 , and it is no longer just applicable to mathematics. Fractional derivatives are the standardization of classical derivatives.…”

Section: Introductionmentioning

confidence: 99%

Impact of nanoparticles on vegetable oil as a cutting fluid with fractional ramped analysis

Hasin

Ahmad

Ali

et al. 2023

Sci Rep

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Better electrical insulation and thermal properties of vegetable oil with nanoparticles are crucial for its uses as a replacement for conventional previous lubricants used in heavy and light industries for cutting and machining. In this study, a magnetohydrodynamic (MHD) flow of a Brinkman-type nanofluid is used to investigate an infinite vertical plate with chemical reaction, heat radiation, and MHD flow. In order to improve the machining and cutting powers of regular vegetable oil, four distinct types of nanoparticles were selected to be the base fluid. The problem is modeled by coupled system partial differential equations (PDEs), and the results are generalized by the Caputo-Fabrizio fractional differential operator for the exponential non-singular kernel. In order to prepare nanofluids, four different types of nanoparticles, namely graphene oxide (GO), molybdenum disulfide (MoS2), titanium dioxide (TiO2), and aluminum oxide (Al2O3) are suspended separately in vegetable oil. The results of skin friction, the Nusselt number, and the Sherwood number are computed in various tables. It is found that GO nanoparticles, (followed by MoS2, TiO2, and Al2O3) are the materials that can heat transfer at the maximum rate. The heat transfer rate for GO is found to be the greatest with an enhancement up to 19.83% when 4% of nanoparticles are dispersed, followed by molybdenum disulfide at 16.96%, titanium dioxide at 16.25%, and alumina at 15.80%.

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Dynamics of chaotic system based on image encryption through fractal-fractional operator of non-local kernel

Cited by 18 publications

References 25 publications

Fractal‐fractional analysis and numerical simulation for the heat transfer of ZnO + Al₂O₃ + TiO₂/DW based ternary hybrid nanofluid

Fractal‐fractional analysis and numerical simulation for the heat transfer of ZnO + Al₂O₃ + TiO₂/DW based ternary hybrid nanofluid

On boundary values system of sequential hybrid fractional differential equations

Impact of nanoparticles on vegetable oil as a cutting fluid with fractional ramped analysis

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Dynamics of chaotic system based on image encryption through fractal-fractional operator of non-local kernel

Cited by 18 publications

References 25 publications

Fractal‐fractional analysis and numerical simulation for the heat transfer of ZnO + Al2O3 + TiO2/DW based ternary hybrid nanofluid

Fractal‐fractional analysis and numerical simulation for the heat transfer of ZnO + Al2O3 + TiO2/DW based ternary hybrid nanofluid

On boundary values system of sequential hybrid fractional differential equations

Impact of nanoparticles on vegetable oil as a cutting fluid with fractional ramped analysis

Contact Info

Product

Resources

About

Fractal‐fractional analysis and numerical simulation for the heat transfer of ZnO + Al₂O₃ + TiO₂/DW based ternary hybrid nanofluid

Fractal‐fractional analysis and numerical simulation for the heat transfer of ZnO + Al₂O₃ + TiO₂/DW based ternary hybrid nanofluid