Browsing by Author "Awrejcewicz, Jan"

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Citation Count: Junaid-U-Rehman, Muhammad...et al. (2024). "Analytical, numerical and experimental observation of isolated branches of periodic orbits in 1DOF mechanical parametric oscillator", Journal of Sound and Vibration, Vol. 584.
Analytical, numerical and experimental observation of isolated branches of periodic orbits in 1DOF mechanical parametric oscillator
(2024) Junaid-U-Rehman, Muhammad; Kudra, Grzegorz; Witkowski, Krzysztof; Wasilewski, Grzegorz; Jarad, Fahd; Awrejcewicz, Jan; 234808
The aim of this study is to investigate the dynamic properties of an existing experimental stand of 1DOF mechanical parametric oscillator, with a focus on approximate analytical solutions of the observed isolated branches of periodic orbits. The experimental stand involves a cart moving along a rolling guide, with the stiffness consisting of two components: a time-varying linear element created by a rotating rod with a rectangular cross-section and a nonlinear hardening stiffness caused by magnetic springs. It was demonstrated that a rolling bearing's nonlinear resistance to motion consists of viscous damping and a second component analytically compared to dry friction. The study utilises multiple scales and harmonic balancing methods to provide analytical solutions. It is then successfully validated using numerical simulations and experimental data. The study investigates how dry friction influences oscillator response and applies the modified Mathieu–Duffing equation to represent the system's dynamics. Different branches of periodic orbits are researched to determine their function in energy harvesting and mechanical system improvement. This research demonstrates the distinctions across analytical, numerical, and experimental methodologies, providing a comprehensive understanding of investigating intricate nonlinear systems.
Citation Count: Riaz, Muhammad Bilal;...et.al. (2022). "Double Diffusive Magneto-Free-Convection Flow of Oldroyd-B Fluid over a Vertical Plate with Heat and Mass Flux", Symmetry, Vol.14, No.2.
Double Diffusive Magneto-Free-Convection Flow of Oldroyd-B Fluid over a Vertical Plate with Heat and Mass Flux
(2022) Riaz, Muhammad Bilal; Rehman, Aziz Ur; Awrejcewicz, Jan; Jarad, Fahd; 234808
The purpose of this research is to analyze the general equations of double diffusive magnetofree convection in an Oldroyd-B fluid flow based on the fundamental symmetry that are presented in non-dimensional form and are applied to a moving heated vertical plate as the boundary layer flow up, with the existence of an external magnetic field that is either moving or fixed consistent with the plate. The thermal transport phenomenon in the presence of constant concentration, coupled with a first order chemical reaction under the exponential heating of the symmetry of fluid flow, is analyzed. The Laplace transform method is applied symmetrically to tackle the non-dimensional partial differential equations for velocity, mass and energy. The contribution of mass, thermal and mechanical components on the dynamics of fluid are presented and discussed independently. An interesting property regarding the behavior of the fluid velocity is found when the movement is observed in the magnetic intensity along with the plate. In that situation, the fluid velocity is not zero when it is far and away from the plate. Moreover, the heat transfer aspects, flow dynamics and their credence on the parameters are drawn out by graphical illustrations. Furthermore, some special cases for the movement of the plate are also studied.
Citation Count: Aziz-Ur, Rehman...et al. (2021). "Exact solutions for thermomagetized unsteady non-singularized jeffrey fluid: Effects of ramped velocity, concentration with newtonian heating", Results in Physics, Vol. 26.
Exact solutions for thermomagetized unsteady non-singularized jeffrey fluid: Effects of ramped velocity, concentration with newtonian heating
(2021) Aziz-Ur, Rehman; Riaz, Muhammad Bilal; Awrejcewicz, Jan; Baleanu, Dumitru; 56389
The classical calculus due to the fact that it assumed as the instant rate of change of the output, when the input level changes. Therefore it is not able to include the previous state of the system called memory effect. But in the Fractional Calculus (FC), the rate of change is affected by all points of the considered interval, so it is able to incorporate the previous history/memory effects of any system. Due to the importance of this effect we used the modern concept of the Caputo-Fabrizio fractional derivative on the considered Jeffrey fluid model. In this paper the effect of Newtonian heating, concentration and velocity on unsteady MHD free convective flow of Jeffrey fluid over long vertical an infinite ramped wall nested in porous material are discussed. Exact analytical solutions are derived via Laplace transformation technique for principal equations of energy, concentration and ramped velocity. The prime features of various coherent parameters are deliberated and illuminated with the aid of plotted graphs. A comparative study to show the significance of fractional order model with an integer order model is accomplished. The fractional order model is found to be the best choice for explaining the memory effect of the considered problem. It is identified that temperature distribution, concentration and ramped velocity profiles for fractional model are converges to an ordinary model when fractional parameter tends to integer order, which shows that fractional model is more appropriate to explicate experimental results. © 2021
Citation Count: Aziz-Ur, Rehman...et al. (2021). "Exact solutions for thermomagetized unsteady non-singularized jeffrey fluid: Effects of ramped velocity, concentration with newtonian heating", Results in Physics, Vol. 26.
Exact solutions for thermomagetized unsteady non-singularized jeffrey fluid: Effects of ramped velocity, concentration with newtonian heating
(2021) Aziz-Ur, Rehman; Riaz, Muhammad Bilal; Awrejcewicz, Jan; Baleanu, Dumitru; 56389
The classical calculus due to the fact that it assumed as the instant rate of change of the output, when the input level changes. Therefore it is not able to include the previous state of the system called memory effect. But in the Fractional Calculus (FC), the rate of change is affected by all points of the considered interval, so it is able to incorporate the previous history/memory effects of any system. Due to the importance of this effect we used the modern concept of the Caputo-Fabrizio fractional derivative on the considered Jeffrey fluid model. In this paper the effect of Newtonian heating, concentration and velocity on unsteady MHD free convective flow of Jeffrey fluid over long vertical an infinite ramped wall nested in porous material are discussed. Exact analytical solutions are derived via Laplace transformation technique for principal equations of energy, concentration and ramped velocity. The prime features of various coherent parameters are deliberated and illuminated with the aid of plotted graphs. A comparative study to show the significance of fractional order model with an integer order model is accomplished. The fractional order model is found to be the best choice for explaining the memory effect of the considered problem. It is identified that temperature distribution, concentration and ramped velocity profiles for fractional model are converges to an ordinary model when fractional parameter tends to integer order, which shows that fractional model is more appropriate to explicate experimental results.
Citation Count: Zulqarnain, Rana Muhammad;...et.al. (2022). "Extension of Einstein Average Aggregation Operators to Medical Diagnostic Approach Under q-Rung Orthopair Fuzzy Soft Set", IEEE Access, Vol.10, pp.87923-87949.
Extension of Einstein Average Aggregation Operators to Medical Diagnostic Approach Under q-Rung Orthopair Fuzzy Soft Se
(2022) Zulqarnain, Rana Muhammad; Rehman, Hafiz Khalil Ur; Awrejcewicz, Jan; Ali, Rifaqat; Siddique, Imran; Jarad, Fahd; Iampan, Aiyared; 234808
The paradigm of the soft set (SS) was pioneered by Moldotsov in 1999 by prefixing the parametrization tool in accustomed sets, which yields general anatomy in decision-making (DM) problems. The q-rung orthopair fuzzy soft set (q-ROFSS) is an induced form of the intuitionistic fuzzy soft set (IFSS) and Pythagorean fuzzy soft set (PFSS). It is also a more significant structure to tackle complex and vague information in DM problems than IFSS and PFSS. This manuscript explores new notions based on Einstein's operational laws for q-rung orthopair fuzzy soft numbers (q-ROFSNs). Our main contribution is to investigate some average aggregation operators (AOs), such as q-rung orthopair fuzzy soft Einstein weighted average (q-ROFSEWA) and q-rung orthopair fuzzy soft Einstein ordered weighted average (q-ROFSEOWA) operators. Besides, the fundamental axioms of proposed operators are discussed. Multi-criteria group decision-making (MCGDM) is vigorous in dealing with the compactness of real-world obstacles, and still, the prevailing MCGDM methods constantly convey conflicting consequences. Based on offered AOs, a robust MCGDM approach is deliberated to accommodate the defects of the prevalent MCGDM methodologies under the q-ROFSS setting. Based on the planned MCGDM method, a medical diagnostic procedure is implemented to recognize the nature of certain infections in different patients. The protracted model estimates illustrious score values to determine patients' health compared to prevailing models, which is more helpful for healthcare experts in identifying the severity of diseases in patients. Furthermore, an inclusive comparative analysis is accomplished to ratify the pragmatism and effectiveness of the proposed technique with some formerly standing methods. The consequences gained over comparative studies display that our established method is more proficient than predominant methodologies.
Citation Count: Rehman, Aziz Ur;...et.al. (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, Vol.27, No.1.
Fractional Modeling of Viscous Fluid over a Moveable Inclined Plate Subject to Exponential Heating with Singular and Non-Singular Kernels
(2022) Rehman, Aziz Ur; Riaz, Muhammad Bilal; Rehman, Wajeeha; Awrejcewicz, Jan; Baleanu, Dumitru; 56389
In this paper, a new approach to investigating the unsteady natural convection flow of viscous fluid over a moveable inclined plate with exponential heating is carried out. The mathematical modeling is based on fractional treatment of the governing equation subject to the temperature, velocity and concentration field. Innovative definitions of time fractional operators with singular and non-singular kernels have been working on the developed constitutive mass, energy and momentum equations. The fractionalized analytical solutions based on special functions are obtained by using Laplace transform method to tackle the non-dimensional partial differential equations for velocity, mass and energy. Our results propose that by increasing the value of the Schimdth number and Prandtl number the concentration and temperature profiles decreased, respectively. The presence of a Prandtl number increases the thermal conductivity and reflects the control of thickness of momentum. The experimental results for flow features are shown in graphs over a limited period of time for various parameters. Furthermore, some special cases for the movement of the plate are also studied and results are demonstrated graphically via Mathcad-15 software.
Citation Count: Riaz, Muhammad Bilal;...et.al. (2022).
Fractional Propagation of Short Light Pulses in Monomode Optical Fibers: Comparison of Beta Derivative and Truncated M-Fractional Derivative
(2022) Riaz, Muhammad Bilal; Jhangeer, Adil; Awrejcewicz, Jan; Baleanu, Dumitru; Tahir, Sana; 56389
This study is dedicated to the computation and analysis of solitonic structures of a nonlinear Sasa–Satsuma equation that comes in handy to understand the propagation of short light pulses in the monomode fiber optics with the aid of beta derivative and truncated M-fractional derivative. We employ a new direct algebraic technique for the nonlinear Sasa–Satsuma equation to derive novel soliton solutions. A variety of soliton solutions are retrieved in trigonometric, hyperbolic, exponential, rational forms. The vast majority of obtained solutions represent the lead of this method on other techniques. The prime advantage of the considered technique over the other techniques is that it provides more diverse solutions with some free parameters. Moreover, the fractional behavior of the obtained solutions is analyzed thoroughly by using two and three-dimensional graphs. This shows that for lower fractional orders, i.e., b ¼ 0:1, the magnitude of truncated M-fractional derivative is greater whereas for increasing fractional orders, i.e., b ¼ 0:7 and b ¼ 0:99, the magnitude remains the same for both definitions except for a phase shift in some spatial domain that eventually vanishes and two curves coincide.
Citation Count: Jarad, Fahd;...et.al. (2022). "Investigation of wave solutions and conservation laws of generalized Calogero–Bogoyavlenskii–Schiff equation by group theoretic method", Results in Physics, Vol.37.
Investigation of wave solutions and conservation laws of generalized Calogero–Bogoyavlenskii–Schiff equation by group theoretic method
(2022) Jarad; Jhangeer, Adil; Awrejcewicz, Jan; Riaz, Muhammad Bilal; Junaid-U, Rehman M.; 234808
This work is focused to analyze the generalized Calogero–Bogoyavlenskii–Schiff equation (GCBSE) by the Lie symmetry method. GCBS equation has been utilized to explain the wave profiles in soliton theory. GCBSE was constructed by Bogoyavlenskii and Schiff in different ways (explained in the introduction section). With the aid of Lie symmetry analysis, we have computed the symmetry generators of the GCBSE and commutation relation. We observed from the commutator table, translational symmetries make an Abelian algebra. Then by using the theory of Lie, we have discovered the similarity variables, which are used to convert the supposed nonlinear partial differential equation (NLPDE) into a nonlinear ordinary differential equation (NLODE). Using the new auxiliary method (NAM), we have to discover some new wave profiles of GCBSE in the type of few trigonometric functions. These exits some parameters which we give to some suitable values to attain the different diagrams of some obtained solutions. Further, the GCBSE is presented by non-linear self-adjointness, and conserved vectors are discovered corresponding to each generator.
Citation Count: Rehman, Aziz Ur;...et.al. (2022). "Mittag-Leffler form solutions of natural convection flow of second grade fluid with exponentially variable temperature and mass diffusion using Prabhakar fractional derivative", Case Studies in Thermal Engineering, Vol.34.
Mittag-Leffler form solutions of natural convection flow of second grade fluid with exponentially variable temperature and mass diffusion using Prabhakar fractional derivative
(2022) Rehman, Aziz Ur; Awrejcewicz, Jan; Riaz, Muhammad Bilal; Jarad, Fahd; 234808
In this article, heat source impact on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer second grade fluid near an exponentially accelerated vertical plate with exponentially variable velocity, temperature and mass diffusion through a porous medium. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on newly introduced Prabhakar fractional operator with generalized Fourier's law and Fick's law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as α, Pr, β, Sc, Gr, γ, Gm are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical second grade model, classical Newtonian model and fractional Newtonian model are recovered from Prabhakar fractional second grade fluid. Moreover, compare the results between second grade and Newtonian fluids for both fractional and classical which shows that the movement of the viscous fluid is faster than second grade fluid. Additionally, it is visualized that for both classical second grade and viscous fluid have relatively higher velocity as compared to fractional second grade and viscous fluid.
Citation Count: Ali, Muhammad Tariq;...et.al. (2023). "Numerical Analysis for the Effect of Irresponsible Immigrants on HIV/AIDS Dynamics", Intelligent Automation and Soft Computing, Vol.36, no.2, pp.1479-1496.
Numerical Analysis for the Effect of Irresponsible Immigrants on HIV/AIDS Dynamics
(2023) Ali, Muhammad Tariq; Baleanu, Dumitru; Rafiq, Muhammad; Awrejcewicz, Jan; Ahmed, Nauman; Raza, Ali; Iqbal, Muhammad Sajid; Ahmad, Muhammad Ozair; 56389
The human immunodeficiency viruses are two species of Lentivirus that infect humans. Over time, they cause acquired immunodeficiency syndrome, a condition in which progressive immune system failure allows life-threatening opportunistic infections and cancers to thrive. Human immunodeficiency virus infection came from a type of chimpanzee in Central Africa. Studies show that immunodeficiency viruses may have jumped from chimpanzees to humans as far back as the late 1800s. Over decades, human immunodeficiency viruses slowly spread across Africa and later into other parts of the world. The SusceptibleInfected-Recovered (SIR) models are significant in studying disease dynamics. In this paper, we have studied the effect of irresponsible immigrants on HIV/AIDS dynamics by formulating and considering different methods. Euler, Runge Kutta, and a Non-standard finite difference (NSFD) method are developed for the same problem. Numerical experiments are performed at disease-free and endemic equilibria points at different time step sizes ‘ℎ’. The results reveal that, unlike Euler and Runge Kutta, which fail for large time step sizes, the proposed Non-standard finite difference (NSFD) method gives a convergence solution for any time step size. Our proposed numerical method is bounded, dynamically consistent, and preserves the positivity of the continuous solution, which are essential requirements when modeling a prevalent disease.
Citation Count: Dayan, Fazal;...et.al. (2023). "Numerical Investigation of Malaria Disease Dynamics in Fuzzy Environment", Computers, Materials and Continua, Vol.74, No.2, pp.2345-2361.
Numerical Investigation of Malaria Disease Dynamics in Fuzzy Environment
(2023) Dayan, Fazal; Baleanu, Dumitru; Ahmed, Nauman; Awrejcewicz, Jan; Rafiq, Muhammad; Raza, Ali; Ahmad, Muhammad Ozair; 56389
The application of fuzzy theory is vital in all scientific disciplines. The construction of mathematical models with fuzziness is little studied in the literature. With this in mind and for a better understanding of the disease, an SEIR model of malaria transmission with fuzziness is examined in this study by extending a classical model of malaria transmission. The parameters β and δ, being function of the malaria virus load, are considered fuzzy numbers. Three steady states and the reproduction number of the model are analyzed in fuzzy senses. A numerical technique is developed in a fuzzy environment to solve the studied model, which retains essential properties such as positivity and dynamic consistency. Moreover, numerical simulations are carried out to illustrate the analytical results of the developed technique. Unlike most of the classical methods in the literature, the proposed approach converges unconditionally and can be considered a reliable tool for studying malaria disease dynamics.
Citation Count: Ullah, Naeem;...et.al. (2022). "On soliton solutions of fractional-order nonlinear model appears in physical sciences", AIMS Mathematics, Vol.7, No.5, pp.7421-7440.
On soliton solutions of fractional-order nonlinear model appears in physical sciences
(2022) Ullah, Naeem; Asjad, Muhammad Imran; Awrejcewicz, Jan; Muhammad, Taseer; Baleanu, Dumitru; 56389
In wave theory, the higher dimensional non-linear models are very important to define the physical phenomena of waves. Herein study we have built the various solitons solutions of (4+1)- dimensional fractional-order Fokas equation by using two analytical techniques that is, the Sardarsubequation method and new extended hyperbolic function method. Different types of novel solitons are attained such as, singular soliton, bright soliton, dark soliton, and periodic soliton. To understand the physical behavior, we have plotted 2D and 3D graphs of some selected solutions. From results we concluded that the proposed methods are straightforward, simple, and efficient. Moreover, this paper offers a hint, how we can convert the fractional-order PDE into an ODE to acquire the exact solutions. Also, the proposed methods and results can be help to examine the advance fractional-order models which seem in optics, hydrodynamics, plasma and wave theory etc.
Citation Count: Zulqarnain, Rana Muhammad...et al. (2022). "Some Einstein Geometric Aggregation Operators for q-Rung Orthopair Fuzzy Soft Set With Their Application in MCDM", IEEE Access, Vol. 10, pp. 88469-88494.
Some Einstein Geometric Aggregation Operators for q-Rung Orthopair Fuzzy Soft Set With Their Application in MCDM
(2022) Zulqarnain, Rana Muhammad; Ali, Rifaqat; Awrejcewicz, Jan; Siddique, Imran; Jarad, Fahd; 234808
q-rung orthopair fuzzy soft sets (q-ROFSS) is a progressive form for orthopair fuzzy sets. It is also an appropriate extension of intuitionistic fuzzy soft sets (IFSS) and Pythagorean fuzzy soft sets (PFSS). The strict prerequisite gives assessors too much autonomy to precise their opinions about membership and non-membership values. The q-ROFSS has a wide range of real-life presentations. The q-ROFSS capably contracts with unreliable and ambiguous data equated to the prevailing IFSS and PFSS. It is the most powerful method for amplifying fuzzy data in decision-making. The hybrid form of orthopair q-rung fuzzy sets with soft sets has emerged as a helpful framework in fuzzy mathematics and decision-making. The hybrid structure of q-rung orthopair fuzzy sets with soft sets has occurred as an expedient context in fuzzy mathematics and decision-making. The fundamental impartial of this research is to propose Einstein's operational laws for q-rung orthopair fuzzy soft numbers (q-ROFSNs). The core objective of this research is to develop some geometric aggregation operators (AOs), such as q-rung orthopair fuzzy soft Einstein weighted geometric (q-ROFSEWG), and q-rung orthopair fuzzy soft Einstein ordered weighted geometric (q-ROFSEOWG) operators. We will discuss the idempotency, boundedness, and homogeneity of the proposed AOs. Multi-criteria decision-making (MCDM) is dynamic in dealing with the density of real-world complications. Still, the prevalent MCDM techniques consistently deliver irreconcilable outcomes. Based on the presented AOs, a strong MCDM technique is deliberate to accommodate the flaws of the prevailing MCDM approaches under the q-ROFSS setting. Moreover, an inclusive comparative analysis is executed to endorse the expediency and usefulness of the suggested method with some previously existing techniques. The outcomes gained through comparative studies spectacle that our established approach is more capable than prevailing methodologies.
Citation Count: El-Deeb, Ahmed A.; Baleanu, Dumitru; Awrejcewicz, Jan (2022). "(γ,a)-Nabla Reverse Hardy–Hilbert-Type Inequalities on Time Scales", Symmetry, Vol.14, No.8.
(γ,a)-Nabla Reverse Hardy–Hilbert-Type Inequalities on Time Scales
(2022) El-Deeb, Ahmed A.; Baleanu, Dumitru; Awrejcewicz, Jan; 56389
In this article, using a ((Formula presented.),a)-nabla conformable integral on time scales, we study several novel Hilbert-type dynamic inequalities via nabla time scales calculus. Our results generalize various inequalities on time scales, unifying and extending several discrete inequalities and their corresponding continuous analogues. We say that symmetry plays an essential role in determining the correct methods with which to solve dynamic inequalities.
Citation Count: El-Deeb, Ahmed A.; Baleanu, Dumitru; Awrejcewicz, J. (2022). "(Δ∇)∇-Pachpatte Dynamic Inequalities Associated with Leibniz Integral Rule on Time Scales with Applications",Symmetry, Vol.14, No.9.
(Δ∇)∇-Pachpatte Dynamic Inequalities Associated with Leibniz Integral Rule on Time Scales with Applications
(2022) El-Deeb, Ahmed A.; Baleanu, Dumitru; Awrejcewicz, Jan; 56389
We prove some new dynamic inequalities of the Gronwall–Bellman–Pachpatte type on time scales. Our results can be used in analyses as useful tools for some types of partial dynamic equations on time scales and in their applications in environmental phenomena and physical and engineering sciences that are described by partial differential equations. © 2022 by the authors.