465
Views
0
CrossRef citations to date
0
Altmetric
Original Article

A fractional study with Newtonian heating effect on heat absorbing MHD radiative flow of rate type fluid with application of novel hybrid fractional derivative operator

, , , &
Pages 482-495 | Received 06 Jun 2022, Accepted 09 Aug 2023, Published online: 30 Aug 2023

References

  • Adegbie, K. S., Omowaye, A. J., Disu, A. B., & Animasaun, I. L. (2015). Heat and mass transfer of upper convected Maxwell fluid flow with variable thermo-physical properties over a horizontal melting surface. Applied Mathematics, 06(08), 1362–1379. doi:10.4236/am.2015.68129
  • Alabedalhadi, M., Al-Smadi, M., Al-Omari, S., Baleanu, D., & Momani, S. (2020). Structure of optical soliton solution for nonliear resonant space-time Schrödinger equation in conformable sense with full nonlinearity term. Physica Scripta, 95(10), 105215. doi:10.1088/1402-4896/abb739
  • Al-Smadi, M., Arqub, O. A., & Gaith, M. (2021). Numerical simulation of telegraph and Cattaneo fractional-type models using adaptive reproducing kernel framework. Mathematical Methods in the Applied Sciences, 44(10), 8472–8489. doi:10.1002/mma.6998
  • Al-Smadi, M., Arqub, O. A., & Hadid, S. (2020). Approximate solutions of nonlinear fractional Kundu-Eckhaus and coupled fractional massive Thirring equations emerging in quantum field theory using conformable residual power series method. Physica Scripta, 95(10), 105205. doi:10.1088/1402-4896/abb420
  • Al-Smadi, M., Djeddi, N., Momani, S., Al-Omari, S., & Araci, S. (2021). An attractive numerical algorithm for solving nonlinear Caputo–Fabrizio fractional Abel differential equation in a Hilbert space. Advances in Difference Equations, 2021, 271. doi:10.1186/s13662-021-03428-3
  • Al-Smadi, M., Freihat, A., Arqub, O. A., & Shawagfeh, N. (2015). A novel multistep generalized differential transform method for solving fractional-order Lü chaotic and hyperchaotic systems. Journal of Computational Analysis and Application, 19, 713–724.
  • Altawallbeh, Z., Al-Smadi, M., Komashynska, I., & Ateiwi, A. (2018). Numerical solutions of fractional systems of two-point BVPs by using the iterative reproducing Kernel algorithm. Ukrainian Mathematical Journal, 70(5), 687–701. doi:10.1007/s11253-018-1526-8
  • Aman, S., Al-Mdallal, Q., & Khan, I. (2020). Heat transfer and second order slip effect on MHD flow of fractional Maxwell fluid in a porous medium. Journal of King Saud University, 32(1), 450–458. doi:10.1016/j.jksus.2018.07.007
  • Atangana, A., & Baleanu, D. (2016). New fractional derivative with non-local and non-singular kernel: Theory and application to heat transfer model. Thermal Science, 20(2), 763–769. doi:10.2298/TSCI160111018A
  • Baleanu, D., Fernandez, A., & Akgül, A. (2020). On a fractional operator combining proportional and classical differintegrals. Mathematics, 8(3), 360. doi:10.3390/math8030360
  • Durbin, F. (1974). Numerical inversion of Laplace transforms: An efficient improvement to Dubner and Abate’s method. Computer Journal, 17(4), 371–376. doi:10.1093/comjnl/17.4.371
  • Faraz, N., Khan, Y., & Anjum, A. (2020). Mathematical modelling of unsteady fractional Phan Thien Tanner fluid. Alexandria Engineering Journal, 59(6), 4391–4395. doi:10.1016/j.aej.2020.07.045
  • Faraz, N., Sadaf, M., Akram, G., Zainab, I., & Khan, Y. (2021). Effects of fractional order time derivative on the solitary wave dynamics of the generalized ZK–Burgers equation. Results in Physics, 25, 104217. doi:10.1016/j.rinp.2021.104217
  • Fardi, M., & Khan, Y. (2021). A novel finite difference-spectral method for fractal mobile/immobiletransport model based on Caputo–Fabrizio derivative. Chaos, Solitons and Fractals, 143, 110573. doi:10.1016/j.chaos.2020.110573
  • Farooq, U., Lu, D., Munir, S., Ramzan, M., Suleman, M., & Hussain, S. (2019). MHD flow of Maxwell fluid with nanomaterials due to an exponentially stretching surface. Scientific Reports, 9(1), 7312. doi:10.1038/s41598-019-43549-0
  • Hasan, S., Al-Smadi, M., El-Ajou, A., Momani, S., Hadid, S., & Al-Zhour, Z. (2021). Numerical approach in the Hilbert space to solve a fuzzy Atangana-Baleanu fractional hybrid system. Chaos Solitons Fractals, 143, 110506. doi:10.1016/j.chaos.2020.110506
  • Islam, M. N., & Akbar, M. A. (2018). Closed form exact solutions to the higher dimensional fractional Schrodinger equation via the modified simple equation method. Journal of Applied Mathematics and Physics, 06(01), 90–102. doi:10.4236/jamp.2018.61009
  • Kahshan, M., Lu, D., & Siddiqui, A. M. (2019). A Jeffrey fluid model for a porous-walled channel: Application to flat plate dialyzer. Scientific Reports, 9(1), 1–18. doi:10.1038/s41598-019-52346-8
  • Khan, Y. (2021). Maclaurin series method for fractal differential-difference models arising in coupled nonlinear optical waveguides. Fractals, 29(01), 2150004. doi:10.1142/S0218348X21500043
  • Khan, M., Malik, M. Y., Salahuddin, T., Saleem, S., & Hussain, A. (2019a). Change in viscosity of Maxwell fluid flow due to thermal and solutal stratifications. Journal of Molecular Liquids, 288, 110970. doi:10.1016/j.molliq.2019.110970
  • Khan, Z., Tairan, N., Mashwani, W. K., Rasheed, H. U., Shah, H., & Khan, W. (2019b). MHD and slip effect on two-immiscible third grade fluid on thin film flow over a vertical moving belt. Open Physics, 17(1), 575–586. doi:10.1515/phys-2019-0059
  • Kumam, Poom, Tassaddiq, Asifa, Watthayu, Wiboonsak, Shah, Zahir, Anwar, Talha, Asifa, Modeling and simulation based investigation of unsteady MHD radiative flow of rate type fluid; a comparative fractional analysis, Mathematics and Computers in Simulation, 201, 486–507, 2022. doi:10.1016/j.matcom.2021.02.005
  • Mackosko, C. W. (1994). Rheology: Principles, measurements and applications. New York: VCH Publishers.
  • Maxwell, J. C. (1867). On the dynamical theory of gases. Philosophical Transcations of the Royal Society London, 157, 49–88.
  • Megahed, A. M. (2021). Improvement of heat transfer mechanism through a Maxwell fluid flow over a stretching sheet embedded in a porous medium and convectively heated. Mathematical and Computers Simulation, 187, 97–109. doi:10.1016/j.matcom.2021.02.018
  • Mohebbi, R., Delouei, A. A., Jamali, A., Izadi, M., & Mohamad, A. A. (2019). Pore-scale simulation of non-Newtonian power-law fluid flow and forced convection in partially porous media: Thermal lattice Boltzmann method. Physica A, 525, 642–656. doi:10.1016/j.physa.2019.03.039
  • Momani, S., Djeddi, N., Al-Smadi, M., & Al-Omari, S. (2021). Numerical investigation for Caputo-Fabrizio fractional Riccati and Bernoulli equations using iterative reproducing kernel method. Applied Numerical Mathematics, 170, 418–434. doi:10.1016/j.apnum.2021.08.005
  • Momani, S., Freihat, A., & Al-Smadi, M. (2014). Analytical study of fractional-order multiple chaotic Fitzhugh-Nagumo neurons model using multistep generalized differential transform method. Abstract and Applied Analysis, 2014, 1–10. doi:10.1155/2014/276279
  • Osman, M. S., Korkmaz, A., Rezazadeh, H., Mirzazadeh, M., Eslami, M., & Zhou, Q. (2018). The unified method for conformable time fractional Schrödinger equation with perturbation terms. Chinese Journal of Physics, 56(5), 2500–2506. doi:10.1016/j.cjph.2018.06.009
  • Rajagopal, K. R., Ruzicka, M., & Srinivasa, A. R. (1996). On the Oberbeck–Boussinesq approximation. Mathematical Models and Methods in Applied Sciences, 06(08), 1157–1167. doi:10.1142/S0218202596000481
  • Rehman, A. U., Riaz, M. B., Rehman, W., Awrejcewicz, J., & Baleanu, D. (2022). Fractional modeling of viscous fluid over a moveable inclined plate subject to exponential heating with singular and non-singular kernels. Mathematical and Computational Applications, 27(1), 8. doi:10.3390/mca27010008
  • Rehman, A. U., Shah, Z. H., & Riaz, M. B. (2021a). Application of local and non-local kernels: The Optimal solutions of water-based nanoparticles under ramped conditions. Progress in Fractional Differentiation and Applications, 7(4), 317–335. doi:10.18576/pfda/070410
  • Rehman, A. U., Riaz, M. B., Saeed, S. T., & Yao, S. (2021b) Dynamical analysis of radiation and heat transfer on MHD second grade fluid. Computer Modeling in Engineering & Sciences, 129(2), 689–703. doi:10.32604/cmes.2021.014980
  • Riaz, M. B., Abro, K. A., Abualnaja, K. M., Akgül, A., Rehman, A. U., Abbas, M., & Hamed, Y. S. (2021a). Exact solutions involving special functions for unsteady convective flow of magnetohydrodynamic second grade fluid with ramped conditions. Advances in Difference Equations, 2021(1), 408. doi:10.1186/s13662-021-03562-y
  • Riaz, M. B., Awrejcewicz, J., & Rehman, A. U. (2021b). Functional effects of permeability on oldroyd-B fluid under magnetization: A comparison of slipping and non-slipping solutions. Applied Science, 11(23), 11477. doi:10.3390/app112311477
  • Riaz, M. B., Awrejcewicz, J., Rehman, A. U., & Abbas, M. (2021c). Special functions-based solutions of unsteady convective flow of a MHD Maxwell fluid for ramped wall temperature and velocity with concentration. Advances in Difference Equations, 2021(1), 500. doi:10.1186/s13662-021-03657-6
  • Riaz, M. B., Awrejcewicz, J., Rehman, A. U., & Akgül, A. (2021d). Thermophysical investigation of oldroyd-B fluid with functional effects of permeability: Memory effect study using non-singular kernel derivative approach. Fractal and Fractional, 5(3), 124. doi:10.3390/fractalfract5030124
  • Riaz, M. B., Rehman, A. U., Awrejcewicz, J., & Akgül, A. (2021e). Power law kernel analysis of MHD Maxwell fluid with ramped boundary conditions: Transport phenomena solutions based on special functions. Fractal and Fractional, 5(4), 248. doi:10.3390/fractalfract5040248
  • Shafiq, A., & Khalique, C. M. (2020). Lie group analysis of upper convected Maxwell fluid flow along stretching surface. Alexandria Engineering Journal, 59(4), 2533–2541. doi:10.1016/j.aej.2020.04.017
  • Yang, X. J., Abdel-Aty, M., & Cattani, C. (2019). A new general fractional order derivative with Rabotnov fractional exponential kernel applied to model the anomalous heat. Thermal Science, 23(3 Part A), 1677–1681. doi:10.2298/TSCI180320239Y