Applied Mathematics, Modeling and Simulation, Fluid Flow and Transfer Processes, Religious studies
32
Scopus Publications
Scopus Publications
ARTIFICIAL NEURAL NETWORK AND RADIAL BASIS FUNCTION APPROACHES FOR COMPUTATIONAL ASSESSMENT OF FRACTAL-FRACTIONAL ELECTROOSMOTIC FLOW MODEL SAQIB MURTAZA, HIJAZ AHMAD, KATEŘINA BEŇOVÁ, TOMÁŠ ADAMEC, ACENG SAMBAS, SYED M. HUSSAIN, MUHAMMAD NAWAZ KHAN, M. A. ABDELKAWY Fractals, 2026 Coupled heat and mass transfer in electroosmotic microfluidic systems is difficult to investigate since the phenomenon is nonlinear and exhibits memory effects that cannot be accurately captured by classical integer-order models. The existing literature is mostly based on deterministic numerical methods and is not very keen on the predictive performance of data-driven models, namely artificial neural networks (ANNs), of parameter-sensitive transport processes. This research gap leads to this research that examines a fractal-fractional electroosmotic fluid flow model in a microchannel under sinusoidal wall oscillation and time-varying thermal and concentration fields, to improve the physical realism and predictive performance. The momentum, energy and concentration equations are constructed with proper physical assumptions and generalized with fractal-fractional derivative of singular kernel to include memory effects and geometric heterogeneity. The resulting non-dimensional equations are solved numerically using local radial basis function (LRBF) collocation method that offers a stable, mesh-free and very accurate computational framework to complex transport problems. Furthermore, an ANN-based surrogate model using Levenberg–Marquardt backpropagation algorithm is developed on the data generated by LRBF. The hybrid LRBF-ANN model provides an efficient solution and detailed parametric sensitivity analysis of each parameter, along with effective prediction of the heat and mass transfer characteristics. The ANN model performance is strictly checked through regression analysis, curve fitting, and error histogram analysis, revealing strong agreement with the numerical solution and excellent predictive accuracy. The parametric analysis shows that the fractal-fractional orders have a strong influence on the velocity, temperature distribution and mass diffusion profiles and provide a more expressive and vivid picture of the electroosmotic transport than classical formulations. These findings highlight the usefulness of ANN-assisted modelling of complex heat and mass transfer phenomena and provide a powerful computational tool to optimize electroosmotic transport in microfluidic systems, biomedical engineering systems, lab-on-a-chip systems and thermal management systems.
THERMAL AND SOLUTAL ANALYSIS OF A TERNARY HYBRID NANOFLUID FLOW IN A POROUS CHANNEL: A FRACTAL–FRACTIONAL MODEL SAQIB MURTAZA, ACENG SAMBAS, MUHAMMAD NAWAZ KHAN, MARCEL MIKESKA, JAN NAJSER, SYED M. HUSSAIN, BAHRAM JALILI, WALEED MOHAMMED ABDELFATTAH, HIJAZ AHMAD Fractals, 2026 Enhancing the heat and mass transfer performance of working fluids remains a critical challenge to pursue sustainable and energy-efficient technologies. Although regular working fluids have superior thermo-physical properties to pure base fluids, they often face limitations that hinder their adoption in multifunctional applications. To overcome these challenges, this study develops a novel, comprehensive and physically consistent mathematical model for an unsteady, electrically conducting ternary hybrid nanofluid composed of graphene oxide (GO), cerium oxide (CeO[Formula: see text], and hexagonal boron nitride ([Formula: see text]-BN) suspended in an environmentally friendly ionic liquid (Ethyl-3-methylimidazolium tetrafluoroborate) [EMIM][BF 4 ]. The model integrates magnetic effects, radiation heat transfer, viscous dissipation, Joule heating, and coupled thermo-diffusion effects. A fractal–fractional derivative operator is employed to generalize the governing equations, while the local radial basis functions (RBF) scheme is used to solve them numerically. Computational and graphical results reveal that CeO 2 suppresses the fluid velocity due to increased inertial resistance, while the dispersion of [Formula: see text]-BN significantly enhanced the thermal profile, resulting in a higher Nusselt number. Furthermore, higher values of Dufour and Soret numbers enhance the coupled heat and mass transfer rates, indicating the model’s potential to design advanced heat exchangers and smart cooling devices. These findings provide valuable guidelines for designing compact heat exchangers and thermal energy storage systems for applications in renewable energy and microelectronics cooling.
Thermal Performance Analysis of Trihybrid Nanofluid Model for Advanced Thermal Management Applications Saqib Murtaza, Zubair Ahmad, Naveed Khan, Razi Khan Spectrum of Engineering and Management Sciences, 2025 Trihybrid nanofluids, which is a combination of three different types of nanoparticles dispersed in a base fluid, let to the recent advances among the advanced thermal transport media because of their excellent heat transfer behaviour as well as an improvement in the thermophysical properties. These fluids are very promising for engineering applications where effective thermal management is needed, such as in microelectronics cooling, renewable energy systems and biomedical devices. In the present work, an analysis is performed with respect to the unsteady flow and heat transfer of trihybrid nanofluid including the mixture of Al₂O₃-TiO₂-ZnO nanoparticles suspended in distilled water. A fractal-fractional model is developed to describe the viscous flow in complex time and space. The Laplace transform method is applied to give the exact solution of the model subjected to suitable initial and boundary conditions. The effects of the key parameters, namely the volume fraction, fractional and fractal order, thermal radiation and Schmidt number on the velocity, temperature and concentration profile are investigated in detail. The additions of three nanoparticles together greatly improves the thermal behaviour of the fluid. These results offer useful information for thermal system optimization in a range of technical and industrial applications where accurate heat control is essential.
Fractional-order analysis of voltage and current propagation in lossy transmission lines with thermal feedback Saqib Murtaza, Faculty of Informatics, Computing, Universiti Sultan Zainal Abidin, Campus Besut, Terengganu, 22200, Malaysia, Lilia El Amraoui, Aceng Sambas, Ahmed Mir, Chemseddine Maatki, Muhammad N. Khan, Badr M. Alshammari, Lioua Kolsi, Artificial Intelligence for Sustainability, Islamic Research Center (AIRIS), Universiti Sultan Zainal Abidin, Gongbadak, Terengganu, 21300, Malaysia, Department of Electrical Engineering, College of Engineering, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia, Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Tamansari Gobras, Tasikmalaya, 46196, Indonesia, Department of Chemical, Materials Engineering, College of Engineering, Northern Border University, Arar P.O. Box 1321, Saudi Arabia, Department of Mechanical Engineering, College of Engineering, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia, Jadara University Research Center, Jadara University, 21110, Jordan, Institute of Engineering Mathematics, University Malaysia Perlis (UniMAP), 02600, Malaysia, Department of Electrical Engineering, College of Engineering, University of Ha'il, Ha'il City 81451, Saudi Arabia, Department of Mechanical Engineering, College of Engineering, University of Ha'il, Ha'il City 81451, Saudi Arabia Aims Mathematics, 2025 Transmission lines form the backbone of power and communication networks, yet their behavior cannot be predicted by classical transmission line theory, which neglects thermal feedback and fractional-order dynamics. To address these limitations, we develop an advanced fractal-fractional electro-thermal model of a lossy transmission line to analyze voltage and current propagation under thermal feedback. The model is based on the fractal-fractional derivative in the sense of Caputo and integrates the effects of series resistance, inductance, conductance, and capacitance together with temperature-dependent feedback. The coupled governing equations are derived as fractal-fractional order partial differential equations based on Kirchoff's current law (KCL) and Kirchoff's voltage law (KVL). The equations are solved numerically using the local radial basis functions (LRBF) scheme, a meshfree numerical technique, to investigate the spatio-temporal profiles of voltage, current, and temperature. The numerical results demonstrate that higher resistance and conductance increase both the attenuation and heating, while increasing capacitance reduces voltage propagation but enhances the current propagation. Furthermore, fractional and fractal orders enrich the analysis by introducing memory and dispersive effects. Overall, this study offers a more realistic and predictive framework for evaluating lossy transmission systems, with direct implications for improving reliability, thermal management, and performance in modern electrical and communication infrastructures.
Thermal Performance Analysis of a Nonlinear Couple Stress Ternary Hybrid Nanofluid in a Channel: A Fractal–Fractional Approach Saqib Murtaza, Nidhal Becheikh, Ata Ur Rahman, Aceng Sambas, Chemseddine Maatki, Lioua Kolsi, Zubair Ahmad Nanomaterials, 2024 Nanofluids have improved thermophysical properties compared to conventional fluids, which makes them promising successors in fluid technology. The use of nanofluids enables optimal thermal efficiency to be achieved by introducing a minimal concentration of nanoparticles that are stably suspended in conventional fluids. The use of nanofluids in technology and industry is steadily increasing due to their effective implementation. The improved thermophysical properties of nanofluids have a significant impact on their effectiveness in convection phenomena. The technology is not yet complete at this point; binary and ternary nanofluids are currently being used to improve the performance of conventional fluids. Therefore, this work aims to theoretically investigate the ternary nanofluid flow of a couple stress fluid in a vertical channel. A homogeneous suspension of alumina, cuprous oxide, and titania nanoparticles is formed by dispersing trihybridized nanoparticles in a base fluid (water). The effects of pressure gradient and viscous dissipation are also considered in the analysis. The classical ternary nanofluid model with couple stress was generalized using the fractal–fractional derivative (FFD) operator. The Crank–Nicolson technique helped to discretize the generalized model, which was then solved using computer tools. To investigate the properties of the fluid flow and the distribution of thermal energy in the fluid, numerical methods were used to calculate the solution, which was then plotted as a function of various physical factors. The graphical results show that at a volume fraction of 0.04 (corresponding to 4% of the base fluid), the heat transfer rate of the ternary nanofluid flow increases significantly compared to the binary and unary nanofluid flows.
Numerical insights of fractal–fractional modeling of magnetohydrodynamic Casson hybrid nanofluid with heat transfer enhancement Zubair Ahmad, Serena Crisci, Saqib Murtaza, Gerardo Toraldo Mathematical Methods in the Applied Sciences, 2024 Fractional calculus expands the idea of differentiation to fractional/non‐integer orders of the derivatives. It includes the memory‐dependent and non‐local system's behaviors while fractal–fractional derivatives is the generalization of fractional‐order derivatives which refers to a combination of fractional calculus and fractal geometry. In this article, we have considered the magnetohydrodynamic (MHD) flow of Casson hybrid nanofluid through a vertical open channel with the effect of viscous dissipation and Newtonian heating. The problem is modeled in terms of non‐linear and coupled integer‐order PDEs which is further generalized through fractal–fractional derivative of power law kernel. Due to non‐linearity and complexities, we have adopted the numerical procedure as it is used when the analytical solutions of PDEs are frequently difficult or impossible for complicated situations. We have established the numerical algorithms for both the classical and fractal–fractional‐order model and compared the results. The existence and uniqueness of the model's solution has been shown theoretically. The effect of various embedded parameters on the heat transfer and fluid flow has been simulated and presented through various figures while skin friction and Nusselt number are tabulated. The effect of fractional and fractal parameter is also shown. As the present model is taken for the hybrid nanofluid flow and for the heat transfer applications, we have considered mineral transformer oil as a base fluid while titania and cadmium telluride nanoparticles are dispersed in it. From the results, it is observed that hybrid nanofluid have a better heat transfer enhancement up to 19.71% while the unitary nanofluids are only capable to enhance the heat transfer up to 9%.
Parametric simulations of fractal-fractional non-linear viscoelastic fluid model with finite difference scheme Saqib Murtaza, Emad A. A. Ismail, Fuad A. Awwad, Ebenezer Bonyah, Ahmed M. Hassan, Muhammad Saad Khan, Razi Khan, Zubair Ahmad Aip Advances, 2024 Fractal-fractional derivatives are more general than the fractional derivative and classical derivative in terms of order. Fractal-fractional derivative is used in those models where the classical continuum hypothesis theory fails. More precisely, these derivative operators are used where the surface or space is discontinuous, e.g., porous medium. Fractal-fractional derivative is considered advance tool to analyze the fluid dynamic model more than fractional and classical model. Given the extensive applicability of fractal-fractional derivatives, the current analysis focuses on investigating the behavior of a non-linear Walter’s-B fluid model under the influence of time-varying temperature and concentration During the simulation process, we have also taken into account the effects of first-order chemical reactions, Soret numbers, thermal radiation, Joule heating, and viscous dissipation of energy. A magnetic field with a strength of B0 was applied to the left plate in the transverse direction. The classical mathematical model was first developed using relative constitutive equations and later generalized with the fractal-fractional derivative operator. Numerical solutions to the generalized model have been obtained using the finite difference method. Various graphs are drawn from the obtained numerical solutions to study the influence of physical parameters on the rheology of Walter’s-B fluid. It has been observed that by varying the fractional and fractal order of the generalized model, one can easily derive fractal, fractional, and classical models.
Fractal-fractional analysis and numerical simulation for the heat transfer of ZnO + Al2O3 + TiO2/DW based ternary hybrid nanofluid Saqib Murtaza, Poom Kumam, Thana Sutthibutpong, Panawan Suttiarporn, Thanarak Srisurat, Zubair Ahmad ZAMM Zeitschrift Fur Angewandte Mathematik Und Mechanik, 2024 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 .
A fractal-fractional perspective on chaotic behavior in 4D memristor-nonlinear system Abdul Hamid Ganie, Fahad Aljuaydi, Zubair Ahmad, Ebenezer Bonyah, Naveed Khan, N. S. Alharthi, Saqib Murtaza, Mashael M. AlBaidani Aip Advances, 2024 The use of fractal–fractional derivatives has attracted considerable interest in the analysis of chaotic and nonlinear systems as they provide a unique capability to represent complex dynamics that cannot be fully described by integer-order derivatives. The fractal–fractional derivative with a power law kernel is used in this paper as an analytical tool to analyze the dynamics of a chaotic integrated circuit. Using coupled ordinary differential equations of classical order, the complexity of an integrated circuit is modeled. The classical order model is generalized via fractal–fractional derivatives of the power law kernel. Moreover, this paper is concerned with investigating the Ulam stability of the model and conducting theoretical studies in order to analyze equilibrium points, identify unique solutions, and verify the existence of such solutions. By examining the complex dynamics that result in chaotic behavior, these investigations shed light on the fundamental properties of integrated circuits. For the purpose of exploring the non-linear fractal–fractional order system, a numerical algorithm has been developed to facilitate our analysis. MATLAB software has been used to implement this algorithm, making it possible to carry out detailed simulations. Simulating solutions are accomplished using 2D and 3D portraits, which provide visual and graphical representations of the results. Throughout the simulation phase, particular attention is given to the impact of fractional order parameter and fractal dimension. As a result of this study, we have gained a comprehensive understanding of the behavior of the system and its response to variations in values.
A time fractional model of a Maxwell nanofluid through a channel flow with applications in grease Naveed Khan, Farhad Ali, Zubair Ahmad, Saqib Murtaza, Abdul Hamid Ganie, Ilyas Khan, Sayed M. Eldin Scientific Reports, 2023 Several scientists are interested in recent developments in nanotechnology and nanoscience. Grease is an essential component of many machines and engines because it helps keep them cool by reducing friction between their various elements. In sealed life applications including centralized lubrication systems, electrical motors, bearings, logging and mining machinery, truck wheel hubs, construction, landscaping, and gearboxes, greases are also utilized. Nanoparticles are added to convectional grease to improve its cooling and lubricating properties. More specifically, the current study goal is to investigate open channel flow while taking grease into account as a Maxwell fluid with MoS2 nanoparticles suspended in it. The Caputo-Fabrizio time-fractional derivative is used to convert the issue from a linked classical order PDE to a local fractional model. To determine the precise solutions for the velocity, temperature, and concentration distributions, two integral transform techniques the finite Fourier sine and the Laplace transform technique are jointly utilized. The resultant answers are physically explored and displayed using various graphs. It is important to note that the fractional model, which offers a variety of integral curves, more accurately depicts the flow behavior than the classical model. Skin friction, the Nusselt number, and the Sherwood number are engineering-related numbers that are quantitatively determined and displayed in tabular form. It is determined that adding MoS2 nanoparticles to grease causes a 19.1146% increase in heat transmission and a 2.5122% decrease in mass transfer. The results obtained in this work are compared with published literature for the accuracy purpose.
