Chaotic characteristics of thermal convection at smaller verse larger Prandtl number through fractal and fractional differential operators from nanofluid

References

• Choi SUS. Enhancing thermal conductivity of fluids with nanoparticles. In Proceedings of the ASME Fluids Engineering Division. San Francisco, CA; Nov 1995; 231, 99–105.
   Google Scholar
• Vadasz P. On the homoclinic orbit for convection in a fluid layer heated from below. Int J Heat Mass Transfer. 1999;42(19):3557–3561.
   Web of Science ®Google Scholar
• Vadasz P, Olek S. Weak turbulence and chaos for low Prandtl number gravity driven convection in porous media. Transp Porous Media. 1999;37(1):69–91.
   Web of Science ®Google Scholar
• Jawdat JM, Hashim I. Low Prandtl number chaotic convection in porous media with uniform internal heat generation. Int J Heat Mass Transf. 2010;37(6):629–636.
   Web of Science ®Google Scholar
• Abro KA, Hussain M, Baig MM., et al. An analytic study of Molybdenum Disulfide Nanofluids using modern approach of Atangana-Baleanu fractional derivatives. European Physical Journal Plus. 2017;132(10):439–449.
   Web of Science ®Google Scholar
• Ali Q, Riaz S, Awan AU, et al. A mathematical model for thermography on viscous fluid based on damped thermal flux. Z Naturforschung A. 2021;(3). DOI:10.1515/zna-2020-0322.
   Web of Science ®Google Scholar
• Abro KA, Jose Francisco G-A. Fractional modeling of fin on non-Fourier heat conduction via modern fractional differential operators. Arab J Sci Eng. 2021;(3). DOI:10.1007/s13369-020-05243-6.
   Web of Science ®Google Scholar
• Idris R, Hashim I. Effects of a magnetic field on chaos for low Prandtl number convection in porous media. Nonlinear Dyn. 2010;62(4):905–917.
   Web of Science ®Google Scholar
• Vadasz JJ, Meyer JP, Govender S., et al. Chaotic and periodic natural convection for moderate and high Prandtl numbers in a porous layer subject to vibrations. Transp Porous Media. 2014;103(2):279–294.
   Web of Science ®Google Scholar
• Gupta VK, Bhadauria BS, Hasim I, et al. Chaotic convection in a rotating fluid layer. Alexandria Eng J. 2015;54(4):981–992.
   Google Scholar
• Zhao M, Wang S, Lib SC, et al. Chaotic Darcy-Brinkman convection in afluid saturated porous layersubjected to gravity modulation. Results Phys. 2018 June;9:1468–1480.
   Web of Science ®Google Scholar
• Asif Y, Hulya D, Kashif AA, et al. Role of gilson–pickering equation for the different types of soliton solutions: a nonlinear analysis. European Physical Journal Plus. 2020;135(8):657.
   Web of Science ®Google Scholar
• Aziz UA, Muhammad T, Kashif AA., et al. Multiple soliton solutions with chiral nonlinear schrödinger’s equation in (2+1)-dimensions. European Journal of Mechanics - B/ Fluids. 2020;85:68–75.
   Web of Science ®Google Scholar
• Muhammad T, Aziz UA, Mohamed SO, et al. Abundant periodic wave solutions for fifth-order sawada-kotera equations. Results Phys. 2020;17:103105.
   Web of Science ®Google Scholar
• Abro KA. Numerical study and chaotic oscillations for aerodynamic model of wind turbine via fractal and fractional differential operators. Numerical Methods for Partial Differential Equations. 2020: 1–15. DOI:10.1002/num.22727.
   Web of Science ®Google Scholar
• Aliyu AI, Inc M, Yusuf A, et al. A fractional model of vertical transmission and cure of vector-borne diseases pertaining to the Atangana–Baleanu fractional derivatives. Chaos Solitons Fractals. 2018;116:268–277.
   Web of Science ®Google Scholar
• Abro KA, Imran QM, Ambreen S., et al. Thermal transmittance and thermo-magnetization of unsteady free convection viscous fluid through non-singular differentiations. Phys Scr. 2020;(1). DOI:10.1088/1402-4896/abc981.
   Web of Science ®Google Scholar
• Li Z, Sheikholeslami M, Jafaryar M, et al. Investigation of nanofluid entropy generation in a heat exchanger with helical twisted tapes. J Mol Liq. 2018;266:797–805.
   Web of Science ®Google Scholar
• Qasim A, Samia R, Aziz UA, et al. Thermal investigation for electrified convection flow of newtonian fluid subjected to damped thermal flux on a permeable medium. Phys Scr. 2020. DOI:10.1088/1402-4896/abbc2e.
   Web of Science ®Google Scholar
• Prathvi RC, Krishan K, Rajan K, et al. Effect of thermophysical property variation on entropy generation towards micro-scale. J Non-Equilib Thermodyn. 2019. DOI:10.1515/jnet-2019-0033.
   Web of Science ®Google Scholar
• Kashif AA. Role of fractal-fractional derivative on ferromagnetic fluid via fractal laplace transform: a first problem via fractal–fractional differential operator. European Journal of Mechanics/B Fluids. 2021;85:76–81.
   Web of Science ®Google Scholar
• Khader M, Saad K, Hammouch Z, et al. A spectral collocation method for solving fractional KdV and KdV-burgers equations with non-singular kernel derivatives. Applied Numerical Mathematics. 2020: 161. DOI:10.1016/j.apnum.2020.10.024.
   Web of Science ®Google Scholar
• Imran QM, Abro KA, Muhammad AS, et al. Functional shape effects of nanoparticles on nanofluid suspended in ethylene glycol through mittage-leffler approach. Phys Scr. 2020;96(2):025005.
   Web of Science ®Google Scholar
• Hristov J. On the Atangana–Baleanu Derivative and Its Relation to the Fading Memory Concept: the Diffusion Equation Formulation. In: José Francisco Gómez-Aguilar, editors. Fractional Derivatives with Mittag-Leffler Kernel. Cham (Switzerland): Springer; 2019. p. 175–193.
   Google Scholar
• Kashif AA. Fractional characterization of fluid and synergistic effects of free convective flow in circular pipe through hankel transform. Phys Fluids. 2020;32(12):123102.
   Web of Science ®Google Scholar
• Ganesh Kumar K, Mohammad Rahimi-Gorj R-G, Gnaneswara Reddy MG, Ali J. Chamkha, Ibrahim M. Alarifi, et al. Enhancement of heat transfer in a convergent/divergent channel by using carbon nanotubes in the presence of a darcy–forchheimer medium. Microsyst Technol. 2019. DOI:10.1007/s00542-019-04489-x.
   Web of Science ®Google Scholar
• Abro KA, Ambreen S, Basma S, et al. Application of statistical method on thermal resistance and conductance during magnetization of fractionalized free convection flow. Int J Heat Mass Transf. 2020;119:104971.
   Web of Science ®Google Scholar
• Atangana A, Araz SI. Extension of atangana-seda numerical method to partial differential equations with integer and non-integer order. Alexandria Eng J. 2020 August;59(4):2355–2370.
   Web of Science ®Google Scholar
• Abro KA, Soomro M, Atangana A, et al. Thermophysical properties of maxwell nanoluids via fractional derivatives with regular kernel. J Therm Anal Calorim. 2020. DOI:10.1007/s10973-020-10287-9.
   Web of Science ®Google Scholar
• Hristov J. Non-linear heat conduction with ramped surface heating ramp surface heating and approximate solution. Therm Sci. 2020;24(Suppl. 1):S377–S389.
   Web of Science ®Google Scholar
• Abro KA, Abdon A. Dual fractional modeling of rate type fluid through non-local differentiation. Numerical Methods Partial Differential Equations. 2020: 1–16. DOI:10.1002/num.22633.
   Web of Science ®Google Scholar
• Gomez-Aguilar JF. Chaos and multiple attractors in a fractal-fractional shinriki’s oscillator model. Phys A. 2020;539:122918.
   Web of Science ®Google Scholar
• Kashif AA, Atangana A. Numerical and mathematical analysis of induction motor by means of AB–fractal–fractional differentiation actuated by drilling system. Numerical Methods for Partial Differential Equations. 2020: 1–15. DOI:10.1002/num.22618.
   Web of Science ®Google Scholar
• Abro KA, Abdon A. Porous effects on the fractional modeling of magnetohydrodynamic pulsatile flow: an analytic study via strong kernels. J Therm Anal Calorim. 2020. DOI:10.1007/s10973-020-10027-z.
   Web of Science ®Google Scholar
• Saad KM, J F G-A, Almadiy AA., et al. A fractional numerical study on a chronic Hepatitis C virus infection model with immune response. Chaos Solitons Fractals. 2020. DOI:10.1016/J.CHAOS.2020.110062.
   PubMed Web of Science ®Google Scholar
• Kashif AA, Abdon A. Numerical study and chaotic analysis of meminductor and memcapacitor through fractal-fractional differential operator. Arab J Sci Eng. 2020. DOI:10.1007/s13369-020-04780-4.
   Web of Science ®Google Scholar
• Abro KA, Atangana A. A comparative analysis of electromechanical model of piezoelectric actuator through Caputo–Fabrizio and Atangana–Baleanu fractional derivatives. Math Meth Appl Sci. 2020:1–11. DOI:10.1002/mma.6638.
   Web of Science ®Google Scholar
• Behzad G, Gómez-Aguilar JF. Two efficient numerical schemes for simulating dynamical systems and capturing chaotic behaviors with Mittag-Leffer memory. Eng Comput. October 2020. DOI:10.1007/s00366-020-01170-0.
   Web of Science ®Google Scholar
• Abro KA, Jose Francisco G-A. Role of fourier sine transform on the dynamical model of tensioned carbon nanotubes with fractional operator. Math Meth Appl Sci. 2020:1–11. DOI:10.1002/mma.6655.
   Web of Science ®Google Scholar
• Abro KA, Atangana A, Jose Francisco G-A., et al. An analytic study of bioheat transfer pennes model via modern non-integers differential techniques. European Physical Journal Plus. 2021;136(11):1144.
   Web of Science ®Google Scholar
• Jose Francisco GA, Hernández MM. Space-time fractional diffusion-advection equation with caputo derivative. Abstract and Applied Analysis. 2014;2014. Hindawi.
   Google Scholar
• Pandey P, Kumar S, Gómez-Aguilar JF, et al. An efficient technique for solving the space-time fractional reaction-diffusion equation in porous media. Chin J Phys. 2020. DOI:10.1016/j.cjph.2020.09.031.
   Web of Science ®Google Scholar
• Pandey P, José Francisco G-A. On solution of a class of nonlinear variable order fractional reaction-diffusion equation with Mittag-Leffler kernel. Numerical Methods for Partial Differential Equations. 2020. https://doi.org/10.1002/num.22563
   Web of Science ®Google Scholar
• Kashif AA, Atangana A. Synchronization via fractal-fractional differential operators on two-mass torsional vibration system consisting of motor and roller. J Comput Nonlin Dyn. 2021. DOI:10.1115/1.4052189.
   PubMed Web of Science ®Google Scholar
• Shamshuddin MD, Mabood F, Anwar OB., et al. Thermomagnetic reactive ethylene-glycol-metallic nanofluid transport from a convectively heated porous surface with ohmic dissipation, heat source, thermophoresis, and brownian motion effects. Int J Model Simulat. 2021. DOI:10.1080/02286203.2021.1977531.
   Google Scholar
• Durur H, Yokus A, Abro KA., et al. Computational and traveling wave analysis of tzitzéica and dodd-bullough-mikhailov equations: an exact and analytical study. Nonlin Eng. 2021;10(1):272–281.
   Google Scholar
• Punith Gowda RJ, Mallikarjuna HB, Prasannakumara BC, et al. Dynamics of thermal marangoni stagnation point flow in dusty casson nanofluid. Int J Model Simulat. 2021. https://doi.org/10.1080/02286203.2021.1957330
   Google Scholar
• Abro KA, Atangana A. Strange attractors and optimal analysis of chaotic systems based on fractal verses fractional differential operators. Int J Model Simulat. 2021. DOI:10.1080/02286203.2021.1966729.
   Google Scholar
• Fatunmbi EO, Salawu SO. Analysis of hydromagnetic micropolar nanofluid flow past a nonlinear stretchable sheet and entropy generation with navier slips. Int J Model Simulat. 2021. DOI:10.1080/02286203.2021.1905490.
   Google Scholar
• Yokus A, Durur H, Abro KA., et al. Role of shallow water waves generated by modified camassa-holm equation: a comparative analysis for traveling wave solutions. Nonlin Eng. 2021;10(1):385–394.
   Google Scholar
• Atangana A. Fractal-fractional differentiation and integration: connecting fractal calculus and fractional calculus to predict complex system. Chaos Soliton Fract. 2017;102:396–406.
   Web of Science ®Google Scholar