Browsing by Author "Ullah, Malik Zaka"

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Citation Count: Alshomrani, Ali Saleh; Ullah, Malik Zaka; Baleanu, Dumitru (2021). "A new approach on the modelling, chaos control and synchronization of a fractional biological oscillator", Advances in Difference Equations, Vol. 2021, No. 1.
A new approach on the modelling, chaos control and synchronization of a fractional biological oscillator
(2021) Alshomrani, Ali Saleh; Ullah, Malik Zaka; Baleanu, Dumitru; 56389
This research aims to discuss and control the chaotic behaviour of an autonomous fractional biological oscillator. Indeed, the concept of fractional calculus is used to include memory in the modelling formulation. In addition, we take into account a new auxiliary parameter in order to keep away from dimensional mismatching. Further, we explore the chaotic attractors of the considered model through its corresponding phase-portraits. Additionally, the stability and equilibrium point of the system are studied and investigated. Next, we design a feedback control scheme for the purpose of chaos control and stabilization. Afterwards, we introduce an efficient active control method to achieve synchronization between two chaotic fractional biological oscillators. The efficiency of the proposed stabilizing and synchronizing controllers is verified via theoretical analysis as well as simulations and numerical experiments.
Citation Count: Baleanu, Dumitru; Alshomrani, Ali Saleh; Ullah, Malik Zaka (2021). "A new fourth-order integrable nonlinear equation: breather, rogue waves, other lump interaction phenomena, and conservation laws", Advances in Difference Equations, Vol. 2021, No. 1.
A new fourth-order integrable nonlinear equation: breather, rogue waves, other lump interaction phenomena, and conservation laws
(2021) Baleanu, Dumitru; Alshomrani, Ali Saleh; Ullah, Malik Zaka; 56389
In this study, we investigate a new fourth-order integrable nonlinear equation. Firstly, by means of the efficient Hirota bilinear approach, we establish novel types of solutions which include breather, rogue, and three-wave solutions. Secondly, with the aid of Lie symmetry method, we report the invariance properties of the studied equation such as the group of transformations, commutator and adjoint representation tables. A differential substitution is found by nonlinear self-adjointness (NSA) and thereafter the associated conservation laws are established. We show some dynamical characteristics of the obtained solutions through via the 3-dimensional and contour graphs.
Citation Count: Ullah, M.Z...et al. (2020). "A New Fractional Study On the Chaotic Vibration and State-Feedback Control of A Nonlinear Suspension System", Chaos, Solitons and Fractals, Vol. 132.
A New Fractional Study On the Chaotic Vibration and State-Feedback Control of A Nonlinear Suspension System
(Elsevier LTD., 2020) Ullah, Malik Zaka; Mallawi, Fouad; Baleanu, Dumitru; Alshomrani, Ali Saleh; 56389
This paper aims to establish a new fractional model to identify the complex behaviors of a magnetorheological suspension system under the road excitation of sinusoidal function. In the new model, we employ a recently introduced fractional operator with Mittag–Leffler kernel. To implement the model, we develop an efficient approximation scheme and discuss its stability and convergence analysis. We identify the complex behaviors by using the analysis of time-domain responses and phase portraits. The results show that the new fractional model has a strong capability to identify different characteristics of the system under investigation, including chaotic and nonchaotic behaviors. Finally, to avoid the chaotic vibration, a state-feedback controller is designed and its efficiency is proved by some simulation experiments.
Citation Count: Baleanu, Dumitru...et al. (2021). "A new generalization of the fractional Euler-Lagrange equation for a vertical mass-spring-damper", Journal of Vibration and Control, Vol. 27, No. 21-22, pp. 2513-2522.
A new generalization of the fractional Euler-Lagrange equation for a vertical mass-spring-damper
(2021) Baleanu, Dumitru; Ullah, Malik Zaka; Mallawi, Fouad; Alshomrani, Ali Saleh; 56389
In this new study, we investigate the motion of a forced mass-spring-damper in a vertical position. First, the classical Lagrangian as well as the classical Euler-Lagrange equation of motion are constructed. Then the fractional Euler-Lagrange equation is derived by extending the classical Lagrangian in the fractional sense. In this extension, a new form of the fractional derivative is employed including a general function as its kernel. The derived fractional Euler-Lagrange equation is then converted into a system of linear algebraic equation by designing an efficient matrix approximation approach. The numerical findings are reported verifying the theoretical investigations. According to the results, some remarkable thinks are achieved; indeed, the numerical simulations show that different aspects of the system under study can be explored with regard to the flexibility found in selecting the kernel contrary to the traditional fractional models.
Citation Count: Ullah, Malik Zaka; Baleanu, Dumitru (2020). "A new type of equation of motion and numerical method for a harmonic oscillator with left and right fractional derivatives", Chinese Journal of Physics, Vol. 68, pp. 712-722.
A new type of equation of motion and numerical method for a harmonic oscillator with left and right fractional derivatives
(2020) Ullah, Malik Zaka; Baleanu, Dumitru; 56389
The aim of this research is to propose a new fractional Euler-Lagrange equation for a harmonic oscillator. The theoretical analysis is given in order to derive the equation of motion in a fractional framework. The new equation has a complicated structure involving the left and right fractional derivatives of Caputo-Fabrizio type, so a new numerical method is developed in order to solve the above-mentioned equation effectively. As a result, we can see different asymptotic behaviors according to the flexibility provided by the use of the fractional calculus approach, a fact which may be invisible when we use the classical Lagrangian technique. This capability helps us to better understand the complex dynamics associated with natural phenomena.
Citation Count: Sabir, Zulqurnain...et al. (2023). "A novel radial basis procedure for the SIRC epidemic delay differential model", International Journal Of Computer Mathematics, Vol.100, No. 10, pp. 2014-2025.
A novel radial basis procedure for the SIRC epidemic delay differential model
(2023) Sabir, Zulqurnain; Baleanu, Dumitru; Mallawi, Fouad Othman; Ullah, Malik Zaka; 56389
The purpose of this work is to construct a reliable stochastic framework for solving the SIRC delay differential epidemic system, i.e. SIRC-DDES that is based on the coronavirus dynamics. The design of radial basis (RB) transfer function with the optimization of Bayesian regularization neural network (RB-BRNN) is presented to solve the SIRC-DDES. The SIRC-DDES is classified into susceptible $ S(x) $ S(x), infected $ I(x) $ I(x), recovered $ R(x) $ R(x) and cross-immune $ C(x) $ C(x). The exactness of the RB-BRNN is performed for three cases of SIRC-DDES by using the performances of the obtained and reference results. The mean square error is reduced by using the training, testing and substantiation performances with the reference solutions. The small values of the absolute error around 10-07 to 10-08 and different statistical operator performances based on the error histogram values, transitions of state investigations, correlation and regression tests also approve the accuracy of the proposed technique.
Citation Count: Ullah, M.Z.; Serra-Capizzano, S.; Baleanu, D.,"A Numerical Simulation for Darcy-Forchheimer Flow of Nanofluid By A Rotating Disk With Partial Slip Effects", Frontiers in Physics, Vol. 7, (2020).
A Numerical Simulation for Darcy-Forchheimer Flow of Nanofluid By A Rotating Disk With Partial Slip Effects
(Frontiers Media S.A., 2020) Ullah, Malik Zaka; Serra-Capizzano, S.; Baleanu, Dumitru; 56389
This study examines Darcy-Forchheimer 3D nanoliquid flow caused by a rotating disk with heat generation/absorption. The impacts of Brownian motion and thermophoretic are considered. Velocity, concentration, and thermal slips at the surface of the rotating disk are considered. The change from the non-linear partial differential framework to the non-linear ordinary differential framework is accomplished by utilizing appropriate variables. A shooting technique is utilized to develop a numerical solution of the resulting framework. Graphs have been sketched to examine how the concentration and temperature fields are affected by several pertinent flow parameters. Skin friction and local Sherwood and Nusselt numbers are additionally plotted and analyzed. Furthermore, the concentration and temperature fields are enhanced for larger values of the thermophoresis parameter. © Copyright © 2020 Ullah, Serra-Capizzano and Baleanu.
Citation Count: Ullah, Malik Zaka; Alzahrani, Abdullah K.; Baleanu, Dumitru, "An efficient numerical technique for a new fractional tuberculosis model with nonsingular derivative operator", Journal of Taibah University For Science, Vol. 13, No. 1, pp. 1147-1157, (2019).
An efficient numerical technique for a new fractional tuberculosis model with nonsingular derivative operator
(Taylor&Francis LTD, 2019) Ullah, Malik Zaka; Alzahrani, Abdullah K.; Baleanu, Dumitru; 56389
The present study aims to investigate a new fractional model describing the dynamical behaviour of the tuberculosis infection. In this new formulation, we use a recently introduced fractional operator with Mittag-Leffler nonsingular kernel. To solve and simulate the proposed model, a new and efficient numerical method is developed based on the product-integration rule. Simulation results are provided and some discussions are given to verify the theoretical analysis. The results indicate that employing the nonsingular operator can extract the hidden aspects of the model under consideration while these features are invisible when we use the ordinary time-derivatives. Therefore, the non-integer calculus supplies more flexible models describing the asymptotic behaviours of the real-world phenomena and helps us to better understand their complex dynamics.
Citation Count: Alghamdi, Metib...et al. (2020). "Dynamics of COVID-19 via singular and non-singular fractional operators under real statistical observations", Mathematical Methods in the Applied Sciences.
Dynamics of COVID-19 via singular and non-singular fractional operators under real statistical observations
(2020) Alghamdi, Metib; Alqarni, M. S.; Alshomrani, Ali Saleh; Ullah, Malik Zaka; Baleanu, Dumitru; 56389
Coronavirus has paralyzed various socio-economic sectors worldwide. Such unprecedented outbreak was proved to be lethal for about 1,069,513 individuals based upon information released by Worldometers on October 09, 2020. In order to fathom transmission dynamics of the virus, different kinds of mathematical models have recently been proposed in literature. In the continuation, we have formulated a deterministic COVID-19 model under fractional operators using six nonlinear ordinary differential equations. Using fixed-point theory and Arzela Ascoli principle, the proposed model is shown to have existence of unique solution while stability analysis for differential equations involved in the model is carried out via Ulam-Hyers and generalized Ulam-Hyers conditions in a Banach space. Real COVID-19 cases considered from July 01 to August 14, 2020, in Pakistan were used to validate the model, thereby producing best fitted values for the parameters via nonlinear least-squares approach while minimizing sum of squared residuals. Elasticity indices for each parameter are computed. Two numerical schemes under singular and non-singular operators are formulated for the proposed model to obtain various simulations of particularly asymptomatically infectious individuals and of control reproduction number Rc. It has been shown that the fractional operators with order alpha=9.8254e-01 generated Rc=2.5087 which is smaller than the one obtained under the classical case ( alpha=1). Interesting behavior of the virus is explained under fractional case for the epidemiologically relevant parameters. All results are illustrated from biological viewpoint.
Citation Count: Alshomrani, Ali Saleh; Ullah, Malik Zaka; Baleanu, Dumitru (2020). "Importance of multiple slips on bioconvection flow of cross nanofluid past a wedge with gyrotactic motile microorganisms", Case Studies in Thermal Engineering, Vol. 22.
Importance of multiple slips on bioconvection flow of cross nanofluid past a wedge with gyrotactic motile microorganisms
(2020) Alshomrani, Ali Saleh; Ullah, Malik Zaka; Baleanu, Dumitru; 56389
In the current article, a mathematical model is developed to visualize the flow of non-Newtonian magneto cross nanofluid with mass and heat transport rates having activation energy, motile microorganisms and bioconvection over the wedge. The phenomena of microorganisms is implemented to control the suspension of nanomaterials. The results of hydromagnetic are also integrated into the momentum expression. Nanofluid is developed by dispersing the nanosized particles in the regular fluid. Nanosized solid materials like carbides, ceramics, graphene, metal, alloyed CNTs etc. have been utilized for the preparation of nanofluid. Physically regular fluids have low thermal efficiency. Therefore, the nanosize particles can be utilized to enhance the thermal efficiency of the regular fluids. Nanofluids have many features in hybrid power engine, heat transfer and can be useful in cancer therapy and medicine. The constructed system is first simplified into nonlinear form by introducing similarity variables. Then obtained ordinary differential equations (ODEs) which are evaluated for numerical solution. Further, for numerical approximation, the popular bvp4c scheme built-in function in MATLAB is utilized. Reliable outcomes are achieved for the temperature, velocity, concentration and motile microorganism density profiles. Results for numerous essential flow parameters are shown via numerical outcomes and graphs. It is revealed that velocity upsurges with enhancement in mixed convection parameter while reduces for bioconvection Rayleigh and buoyancy ratio parameters. Furthermore, the volumetric concentration of nanoparticles boost up for growing estimations of activation energy parameter. The microorganisms field upsurges with larger microorganism slip parameters while reduces with the augmentation in magnitude of bioconvection Lewis number and Peclet number. The obtained numerical results are compared with the available data and found good agreement. © 2020 The Author(s).
Citation Count: Ullah, Malik Zaka; Al-Aidarous, Eman S.; Baleanu, Dumitru, "New Aspects of Immunogenic Tumors Within Different Fractional Operators", Journal of Computatonal and Nonlinear Dynamics, Vol. 14, No. 4, (2019).
New Aspects of Immunogenic Tumors Within Different Fractional Operators
(ASME, 2019) Ullah, Malik Zaka; Al-Aidarous, Eman S.; Baleanu, Dumitru; 56389
This paper presents a new mathematical formulation in fractional sense describing the asymptotic behavior of immunogenic tumor growth. The new model is investigated through different fractional operators with and without singular kernel. An efficient numerical technique to solve these equations is also suggested. Comparative results with experimental data verify that the fractional-order growth model covers the real data better than the integer model of tumor growth. Thus, more precise models can be provided by the fractional calculus (FC), which helps us to examine better the complex dynamics. Finally, numerical results confirming the theoretical analysis are provided.