Browsing by Author "Iqbal, Muhammad Kashif"

Now showing 1 - 8 of 8

Citation Count: Rashid, Saima;...et.al. (2022). "A comprehensive analysis of the stochastic fractal–fractional tuberculosis model via Mittag-Leffler kernel and white noise", Results in Physics, Vol.39.
A comprehensive analysis of the stochastic fractal–fractional tuberculosis model via Mittag-Leffler kernel and white noise
(2022) Rashid, Saima; Iqbal, Muhammad Kashif; Alshehri, Ahmed M.; Ashraf, Rehana; Jarad, Fahd; 234808
In this research, we develop a stochastic framework for analysing tuberculosis (TB) evolution that includes newborn immunization via the fractal–fractional (F–F) derivative in the Atangana–Baleanu sense. The population is divided into four groups by this system: susceptibility S(ξ), infectious I(ξ), immunized infants V(ξ), and restored R(ξ). The stochastic technique is used to describe and assess the invariant region, basic reproduction number, and local stability for disease-free equilibrium. This strategy has significant modelling difficulties since it ignores the unpredictability of the system phenomena. To prevent such problems, we convert the deterministic strategy to a randomized one, which seems recognized to have a vital influence by adding an element of authenticity and fractional approach. Owing to the model intricacies, we established the existence-uniqueness of the model and the extinction of infection was carried out. We conducted a number of experimental tests using the F–F derivative approach and obtained some intriguing modelling findings in terms of (i) varying fractional-order (φ) and fixing fractal-dimension (ω), (ii) varying ω and fixing φ, and (iii) varying both φ and ω, indicating that a combination of such a scheme can enhance infant vaccination and adequate intervention of infectious patients can give a significant boost.
Citation Count: Amin, Muhammad...et al. (2019) "A Fourth Order Non-Polynomial Quintic Spline Collocation Technique for Solving Time Fractional Superdiffusion Equations", Advances in Difference Equations, Vol. 2019, No. 1.
A Fourth Order Non-Polynomial Quintic Spline Collocation Technique for Solving Time Fractional Superdiffusion Equations
(Springer, 2019) Amin, Muhammad; Abbas, Muhammad; Iqbal, Muhammad Kashif; Ismail, Ahmad Izani Md.; Baleanu, Dumitru; 56389
The purpose of this article is to present a technique for the numerical solution of Caputo time fractional superdiffusion equation. The central difference approximation is used to discretize the time derivative, while non-polynomial quintic spline is employed as an interpolating function in the spatial direction. The proposed method is shown to be unconditionally stable and O(h4+ Δ t2) accurate. In order to check the feasibility of the proposed technique, some test examples have been considered and the simulation results are compared with those available in the existing literature. © 2019, The Author(s).
Citation Count: Khalid, Nauman...et al. (2019). "A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms", Advances in Difference Equations, Vol. 2019, No. 1.
A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms
(Springer Open, 2019) Khalid, Nauman; Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru; 56389
In this study, we have proposed an efficient numerical algorithm based on third degree modified extended B-spline (EBS) functions for solving time-fractional diffusion wave equation with reaction and damping terms. The Caputo time-fractional derivative has been approximated by means of usual finite difference scheme and the modified EBS functions are used for spatial discretization. The stability analysis and derivation of theoretical convergence validates the authenticity and effectiveness of the proposed algorithm. The numerical experiments show that the computational outcomes are in line with the theoretical expectations. Moreover, the numerical results are proved to be better than other methods on the topic.
Citation Count: Khalid, Nauman...et al. (2020). "A numerical investigation of Caputo time fractional Allen-Cahn equation using redefined cubic B-spline functions", Advances in Difference Equations, Vol. 2020, No. 1.
A numerical investigation of Caputo time fractional Allen-Cahn equation using redefined cubic B-spline functions
(2020) Khalid, Nauman; Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru; 56389
We present a collocation approach based on redefined cubic B-spline (RCBS) functions and finite difference formulation to study the approximate solution of time fractional Allen-Cahn equation (ACE). We discretize the time fractional derivative of order alpha is an element of (0,1] by using finite forward difference formula and bring RCBS functions into action for spatial discretization. We find that the numerical scheme is of order O(h2+Delta t2-alpha) and unconditionally stable. We test the computational efficiency of the proposed method through some numerical examples subject to homogeneous/nonhomogeneous boundary constraints. The simulation results show a superior agreement with the exact solution as compared to those found in the literature.
Citation Count: Amin, Muhammad...et al. (2019). "Non-polynomial quintic spline for numerical solution of fourth-order time fractional partial differential equations", Advances in Difference Equations.
Non-polynomial quintic spline for numerical solution of fourth-order time fractional partial differential equations
(Springer Open, 2019) Amin, Muhammad; Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru; 56389
This paper presents a novel approach to numerical solution of a class of fourth-order time fractional partial differential equations (PDEs). The finite difference formulation has been used for temporal discretization, whereas the space discretization is achieved by means of non-polynomial quintic spline method. The proposed algorithm is proved to be stable and convergent. In order to corroborate this work, some test problems have been considered, and the computational outcomes are compared with those found in the exiting literature. It is revealed that the presented scheme is more accurate as compared to current variants on the topic.
Citation Count: Amin, Muhammad...et al. (2020). "Numerical Treatment of Time-Fractional Klein–Gordon Equation Using Redefined Extended Cubic B-Spline Functions", Frontiers in Physics, Vol. 8.
Numerical Treatment of Time-Fractional Klein–Gordon Equation Using Redefined Extended Cubic B-Spline Functions
(2020) Amin, Muhammad; Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru; 56389
In this article we develop a numerical algorithm based on redefined extended cubic B-spline functions to explore the approximate solution of the time-fractional Klein–Gordon equation. The proposed technique employs the finite difference formulation to discretize the Caputo fractional time derivative of order α ∈ (1, 2] and uses redefined extended cubic B-spline functions to interpolate the solution curve over a spatial grid. A stability analysis of the scheme is conducted, which confirms that the errors do not amplify during execution of the numerical procedure. The derivation of a uniform convergence result reveals that the scheme is O(h2 + Δt2−α) accurate. Some computational experiments are carried out to verify the theoretical results. Numerical simulations comparing the proposed method with existing techniques demonstrate that our scheme yields superior outcomes.
Citation Count: Amin, Muhammad...et al. (2021). "Redefined extended cubic B-spline functions for numerical solution of time-fractional telegraph equation", CMES - Computer Modeling in Engineering and Sciences, Vol. 127, No. 1, pp. 361-384.
Redefined extended cubic B-spline functions for numerical solution of time-fractional telegraph equation
(2021) Amin, Muhammad; Abbas, Muhammad; Baleanu, Dumitru; Iqbal, Muhammad Kashif; Riaz, Muhammad Bilal; 56389
This work is concerned with the application of a redefined set of extended uniform cubic B-spline (RECBS) functions for the numerical treatment of time-fractional Telegraph equation. The presented technique engages finite difference formulation for discretizing the Caputo time-fractional derivatives and RECBS functions to interpolate the solution curve along the spatial grid. Stability analysis of the scheme is provided to ensure that the errors do not amplify during the execution of the numerical procedure. The derivation of uniform convergence has also been presented. Some computational experiments are executed to verify the theoretical considerations. Numerical results are compared with the existing schemes and it is concluded that the present scheme returns superior outcomes on the topic.
Citation Count: Majeed, Abdul...et al. (2020) "Solving time fractional Burgers' and Fisher's equations using cubic B-spline approximation method", Advances in Difference Equations, Vol. 2020, No. 1.
Solving time fractional Burgers' and Fisher's equations using cubic B-spline approximation method
(2020) Majeed, Abdul; Kamran, Mohsin; Iqbal, Muhammad Kashif; Baleanu, Dumitru; 56389
This article presents a numerical algorithm for solving time fractional Burgers' and Fisher's equations using cubic B-spline finite element method. The L1 formula with Caputo derivative is used to discretized the time fractional derivative, whereas the Crank-Nicolson scheme based on cubic B-spline functions is used to interpolate the solution curve along the spatial grid. The numerical scheme has been implemented on three test problems. The obtained results indicate that the proposed method is a good option for solving nonlinear fractional Burgers' and Fisher's equations. The error norms L2 and L infinity have been calculated to validate the efficiency and accuracy of the presented algorithm.