Applications of fractional derivatives to nanofluids: exact and numerical solutions
Math. Model. Nat. Phenom., 13 1 (2018) 2
Published online: 2018-04-06
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Space-time fractional parabolic equations on a metric star graph with spatial fractional derivative of Sturm-Liouville type: analysis and discretization
Vaibhav Mehandiratta and Mani MehraFractional Calculus and Applied Analysis 28 (2) 862 (2025)
https://doi.org/10.1007/s13540-025-00376-7
Finite difference approximation of time-fractional advection-diffusion equation on a metric star graph
Shweta Kumari, Mani Mehra and Vaibhav MehandirattaInternational Journal of Computer Mathematics 102 (12) 2032 (2025)
https://doi.org/10.1080/00207160.2025.2531521
Application of fractional model computations for a mathematical study of unsteady Williamson ternary-Hybrid nanofluid flow with heat transfer past a stretching orthogonal surface
M.M. Nour, Assma S. Zaki, Waqar A. Khan, A.M. Rashad, Amal M.A. EL-Hakiem, Abdallah aldurayhim, Mohamed M. Awad and Hossam A. NabweyJournal of Engineering Research (2025)
https://doi.org/10.1016/j.jer.2025.10.018
Dual Thermal Analysis of Fractional Convective Flow Through Aluminum Oxide and Titanium Dioxide Nanoparticles
Qasim Ali, Rajai S. Alassar, Irfan. A. Abro and Kashif. A. AbroActa Mechanica et Automatica 19 (1) 32 (2025)
https://doi.org/10.2478/ama-2025-0005
Non-Overlapping Domain Decomposition for 1D Optimal Control Problems Governed by Time-Fractional Diffusion Equations on Coupled Domains: Optimality System and Virtual Controls
Günter Leugering, Vaibhav Mehandiratta and Mani MehraFractal and Fractional 8 (3) 129 (2024)
https://doi.org/10.3390/fractalfract8030129
A new clique polynomial approach for fractional partial differential equations
Waleed Adel and Kumbinarasaiah SrinivasaInternational Journal of Nonlinear Sciences and Numerical Simulation 24 (8) 2839 (2024)
https://doi.org/10.1515/ijnsns-2021-0258
Well‐posedness, optimal control and discretization for time‐fractional parabolic equations with time‐dependent coefficients on metric graphs
Vaibhav Mehandiratta, Mani Mehra and Günter LeugeringAsian Journal of Control 25 (3) 2360 (2023)
https://doi.org/10.1002/asjc.2958
Prabhakar fractional simulation for thermal and solutal transport analysis of a Casson hybrid nanofluid flow over a channel with buoyancy effects
Yuanjian Lin, Ali Raza, Umair Khan, Niat Nigar, Samia Elattar, Afrah M. AlDerea and Hamiden Abd El-Wahed KhalifaJournal of Magnetism and Magnetic Materials 586 171176 (2023)
https://doi.org/10.1016/j.jmmm.2023.171176
Fractional melting process in inclined containers using (NePCM) and hybrid nanoparticles
Sameh E. Ahmed, Shaaban A. Bakr, Z.Z. Rashed and Zehba A.S. RaizahAlexandria Engineering Journal 76 307 (2023)
https://doi.org/10.1016/j.aej.2023.06.016
Influence of nanoparticle shapes on natural convection flow with heat and mass transfer rates of nanofluids with fractional derivative
K.R. Madhura, Babitha Atiwali and S.S. IyengarMathematical Methods in the Applied Sciences 46 (7) 8089 (2023)
https://doi.org/10.1002/mma.7404
An exact solution of heat and mass transfer analysis on hydrodynamic magneto nanofluid over an infinite inclined plate using Caputo fractional derivative model
J. Kayalvizhi, A. G. Vijaya Kumar, Ndolane Sene, et al.AIMS Mathematics 8 (2) 3542 (2023)
https://doi.org/10.3934/math.2023180
Heat Transfer Enhancement through Thermodynamical Activity of H2O/Clay Nanofluid Flow over an Infinite Upright Plate with Caputo Fractional-Order Derivative
J. Kayalvizhi, A. G. Vijaya Kumar, Hakan F. Öztop, Ndolane Sene and Nidal H. Abu-HamdehEnergies 15 (16) 6082 (2022)
https://doi.org/10.3390/en15166082
On Discrete Fractional Complex Gaussian Map: Fractal Analysis, Julia Sets Control, and Encryption Application
Amr Elsonbaty, A. Elsadany, Fatma Kamal and Amin JajarmiMathematical Problems in Engineering 2022 1 (2022)
https://doi.org/10.1155/2022/8148831
Impact of generalized fourier law in thermal flux convective flow over a vertical plate: Analysis of fractional derivative
Ali Raza, Hala A. Hejazi and M. Ijaz KhanInternational Journal of Modern Physics B 36 (24) (2022)
https://doi.org/10.1142/S0217979222501624
A comparative study for fractional simulations of Casson nanofluid flow with sinusoidal and slipping boundary conditions via a fractional approach
Ali Raza, Umair Khan, Aurang Zaib, Wajaree Weera and Ahmed M. GalalAIMS Mathematics 7 (11) 19954 (2022)
https://doi.org/10.3934/math.20221092
Unsteady Casson fluid flow over a vertical surface with fractional bioconvection
Muhammad Imran Asjad, Muhammad Haris Butt, Muhammad Armaghan Sadiq, Muhammad Danish Ikram and Fahd JaradAIMS Mathematics 7 (5) 8112 (2022)
https://doi.org/10.3934/math.2022451
Transport properties of mixed convective nano-material flow considering the generalized fourier law and a vertical surface: Concept of caputo-time fractional derivative
Ali Raza, Sami Ullah Khan, Saadia Farid, Muhammad Ijaz Khan, M Riaz Khan, Absar Ul Haq, Awatif MA Elsiddieg, MY Malik and Shami AM AlsallamiProceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 236 (5) 974 (2022)
https://doi.org/10.1177/09576509221075110
Numerical Solution of Two-Dimensional Time Fractional Mobile/Immobile Equation Using Explicit Group Methods
Fouad Mohammad Salama, Umair Ali and Ajmal AliInternational Journal of Applied and Computational Mathematics 8 (4) (2022)
https://doi.org/10.1007/s40819-022-01408-z
A comprehensive review of nanofluids with fractional derivatives: Modeling and application
Ming Shen, Hui Chen, Mengchen Zhang, Fawang Liu and Vo AnhNanotechnology Reviews 11 (1) 3235 (2022)
https://doi.org/10.1515/ntrev-2022-0496
Swarm Intelligence Procedures Using Meyer Wavelets as a Neural Network for the Novel Fractional Order Pantograph Singular System
Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Juan L. G. Guirao and Tareq SaeedFractal and Fractional 5 (4) 277 (2021)
https://doi.org/10.3390/fractalfract5040277
FRACTIONAL MAYER NEURO-SWARM HEURISTIC SOLVER FOR MULTI-FRACTIONAL ORDER DOUBLY SINGULAR MODEL BASED ON LANE–EMDEN EQUATION
ZULQURNAIN SABIR, MUHAMMAD ASIF ZAHOOR RAJA and DUMITRU BALEANUFractals 29 (05) 2140017 (2021)
https://doi.org/10.1142/S0218348X2140017X
Dynamics of viscoelastic fluid conveying nanoparticles over a wedge when bioconvection and melting process are significant
M. Ijaz Khan and Faris AlzahraniInternational Communications in Heat and Mass Transfer 128 105604 (2021)
https://doi.org/10.1016/j.icheatmasstransfer.2021.105604
Fractional order simulations for the thermal determination of graphene oxide (GO) and molybdenum disulphide (MoS2) nanoparticles with slip effects
Ali Raza, Sami Ullah Khan, M. Ijaz Khan, Saadia Farid, Taseer Muhammad, M. Imran Khan and Ahmed M. GalalCase Studies in Thermal Engineering 28 101453 (2021)
https://doi.org/10.1016/j.csite.2021.101453
Thermal activity of conventional Casson nanoparticles with ramped temperature due to an infinite vertical plate via fractional derivative approach
Ali Raza, Sami Ullah Khan, Saadia Farid, M. Ijaz Khan, Tian-Chuan Sun, Aamar Abbasi, M. Imran Khan and M.Y. MalikCase Studies in Thermal Engineering 27 101191 (2021)
https://doi.org/10.1016/j.csite.2021.101191
Bio-convective thermal melting applications of viscoelastic nanoparticles due to moving wedge
M. Ijaz Khan and Faris AlzahraniCase Studies in Thermal Engineering 28 101493 (2021)
https://doi.org/10.1016/j.csite.2021.101493
Solution of novel multi-fractional multi-singular Lane–Emden model using the designed FMNEICS
Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Juan L. G. Guirao and Tareq SaeedNeural Computing and Applications 33 (24) 17287 (2021)
https://doi.org/10.1007/s00521-021-06318-7
FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system
Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Muhammad Shoaib and J. F. Gómez AguilarComputational and Applied Mathematics 39 (4) (2020)
https://doi.org/10.1007/s40314-020-01350-0
Analytical solutions for free convection flow of Casson nanofluid over an infinite vertical plate
Mushtaq Ahmad, Muhammad Imran Asjad, Ali Akgül and Dumitru BaleanuAIMS Mathematics 6 (3) 2344 (2020)
https://doi.org/10.3934/math.2021142
Mathematical modeling of (Cu−Al2O3) water based Maxwell hybrid nanofluids with Caputo-Fabrizio fractional derivative
M Ahmad, MA Imran and M NazarAdvances in Mechanical Engineering 12 (9) (2020)
https://doi.org/10.1177/1687814020958841
A new approach for the solutions of the fractional generalized Casson fluid model described by Caputo fractional operator
Ndolane SENEAdvances in the Theory of Nonlinear Analysis and its Application 4 (4) 373 (2020)
https://doi.org/10.31197/atnaa.752330
Thermal investigation for electrified convection flow of Newtonian fluid subjected to damped thermal flux on a permeable medium
Qasim Ali, Samia Riaz, Aziz Ullah Awan and Kashif Ali AbroPhysica Scripta 95 (11) 115003 (2020)
https://doi.org/10.1088/1402-4896/abbc2e
2133 030021 (2019)
https://doi.org/10.1063/1.5114005
2133 030012 (2019)
https://doi.org/10.1063/1.5113996
Casson Model of MHD Flow of SA-Based Hybrid Nanofluid Using Caputo Time-Fractional Models
Sidra Aman, Syazwani Mohd Zokri, Zulkhibri Ismail, Mohd Zuki Salleh and Ilyas KhanDefect and Diffusion Forum 390 83 (2019)
https://doi.org/10.4028/www.scientific.net/DDF.390.83