Browsing by Author "Nisar, Kottakkaran Sooppy"

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A note on (p, q)-analogue type of Fubini numbers and polynomials
(2020) Khan, Waseem Ahmad; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru
In this paper, we introduce a new class of (p, q)-analogue type of Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we consider some relationships for (p, q)-Fubini polynomials associated with (p, q)-Bernoulli polynomials, (p, q)-Euler polynomials and (p, q)-Genocchi polynomials and (p, q)-Stirling numbers of the second kind.p>
Citation - WoS: 16
Citation - Scopus: 17
Numerical Analysis of the Susceptible Exposed Infected Quarantined and Vaccinated (Seiqv) Reaction-Diffusion Epidemic Model
(Frontiers Media Sa, 2020) Fatima, Mehreen; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Khan, Ilyas; Rafiq, Muhammad; Ahmad, Muhammad Ozair; Ahmed, Nauman
In this paper, two structure-preserving nonstandard finite difference (NSFD) operator splitting schemes are designed for the solution of reaction diffusion epidemic models. The proposed schemes preserve all the essential properties possessed by the continuous systems. These schemes are applied on a diffusive SEIQV epidemic model with a saturated incidence rate to validate the results. Furthermore, the stability of the continuous system is proved, and the bifurcation value is evaluated. A comparison is also made with the existing operator splitting numerical scheme. Simulations are also performed for numerical experiments.
Citation - WoS: 80
Citation - Scopus: 94
Entropy Generation and Consequences of Mhd in Darcy-Forchheimer Nanofluid Flow Bounded by Non-Linearly Stretching Surface
(Mdpi, 2020) Shafiq, Anum; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Shahzadi, Gullnaz; Rasool, Ghulam
Present communication aims to inspect the entropy optimization, heat and mass transport in Darcy-Forchheimer nanofluid flow surrounded by a non-linearly stretching surface. Navier-Stokes model based governing equations for non-Newtonian nanofluids having symmetric components in various terms are considered. Non-linear stretching is assumed to be the driving force whereas influence of thermal radiation, Brownian diffusion, dissipation and thermophoresis is considered. Importantly, entropy optimization is performed using second law of thermodynamics. Governing problems are converted into nonlinear ordinary problems (ODEs) using suitably adjusted transformations. RK-45 based built-in shooting mechanism is used to solve the problems. Final outcomes are plotted graphically. In addition to velocity, temperature, concentration and Bejan number, the stream lines, contour graphs and density graphs have been prepared. For their industrial and engineering importance, results for wall-drag force, heat flux (Nusselt) rate and mass flux (Sherwood) rate are also given in tabular data form. Outputs indicate that velocity reduces for Forchheimer number as well as for the porosity factor. However, a rise is noted in temperature distribution for elevated values of thermal radiation. Entropy optimization shows enhancement for larger values of temperature difference ratio. Skin-friction enhances for all relevant parameters involved in momentum equation.
Citation - WoS: 19
Citation - Scopus: 25
Construction of Cubic Timmer Triangular Patches and Its Application in Scattered Data Interpolation
(Mdpi, 2020) Karim, Samsul Ariffin Abdul; Saaban, Azizan; Hasan, Mohammad Khatim; Ghaffar, Abdul; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Ali, Fatin Amani Mohd
This paper discusses scattered data interpolation by using cubic Timmer triangular patches. In order to achieve C-1 continuity everywhere, we impose a rational corrected scheme that results from convex combination between three local schemes. The final interpolant has the form quintic numerator and quadratic denominator. We test the scheme by considering the established dataset as well as visualizing the rainfall data and digital elevation in Malaysia. We compare the performance between the proposed scheme and some well-known schemes. Numerical and graphical results are presented by using Mathematica and MATLAB. From all numerical results, the proposed scheme is better in terms of smaller root mean square error (RMSE) and higher coefficient of determination (R-2). The higher R-2 value indicates that the proposed scheme can reconstruct the surface with excellent fit that is in line with the standard set by Renka and Brown's validation.
Citation - WoS: 8
Citation - Scopus: 14
Shape-Preserving Properties of a Relaxed Four-Point Interpolating Subdivision Scheme
(Mdpi, 2020) Ghaffar, Abdul; Baleanu, Dumitru; Sehar, Irem; Nisar, Kottakkaran Sooppy; Khan, Faheem; Ashraf, Pakeeza
In this paper, we analyze shape-preserving behavior of a relaxed four-point binary interpolating subdivision scheme. These shape-preserving properties include positivity-preserving, monotonicity-preserving and convexity-preserving. We establish the conditions on the initial control points that allow the generation of shape-preserving limit curves by the four-point scheme. Some numerical examples are given to illustrate the graphical representation of shape-preserving properties of the relaxed scheme.
Citation - WoS: 15
Citation - Scopus: 18
Analysis of Geometric Properties of Ternary Four-Point Rational Interpolating Subdivision Scheme
(Mdpi, 2020) Nawaz, Bushra; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Ghaffar, Abdul; Khan, Muhammad Aqeel Ahmed; Akram, Saima; Ashraf, Pakeeza
Shape preservation has been the heart of subdivision schemes (SSs) almost from its origin, and several analyses of SSs have been established. Shape preservation properties are commonly used in SSs and various ways have been discovered to connect smooth curves/surfaces generated by SSs to applied geometry. With an eye on connecting the link between SSs and applied geometry, this paper analyzes the geometric properties of a ternary four-point rational interpolating subdivision scheme. These geometric properties include monotonicity-preservation, convexity-preservation, and curvature of the limit curve. Necessary conditions are derived on parameter and initial control points to ensure monotonicity and convexity preservation of the limit curve of the scheme. Furthermore, we analyze the curvature of the limit curve of the scheme for various choices of the parameter. To support our findings, we also present some examples and their graphical representation.
Citation - WoS: 18
Citation - Scopus: 19
On Hybrid Nanofluid Yamada-Ota and Xue Flow Models in a Rotating Channel With Modified Fourier Law
(Nature Portfolio, 2021) Gul, Hina; Malik, M. Y.; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Ramzan, Muhammad
The present study analyzes the comparison of the Xue and Yamada-Ota models for a hybrid nanoliquid flow in porous media occurring amidst a rotating channel with surface catalyzed reaction. Here, the hybrid nanofluid flow is studied under the effect of Cattaneo Christov (C-C) heat flux and homogenous heterogeneous (Homo-Hetero) chemical reaction with entropy generation minimization analysis. The assumptions of the viscosity of hybrid nanomaterial fluid and variable thermal conductivity are added characteristics to the inimitability of the flow model. Two kinds of nanoparticles, namely single-wall carbon nanotubes and multi-wall carbon nanotubes with ethylene glycol (EG) as the base fluid are considered. Carbon nanotubes possess diverse applications in daily life including energy storage, drug delivery, cancer treatment, tissue generation, platelet activation, magnetic force microscopy, and microwave absorption, etc. Similarity transformations are utilized to translate the modeled problem into the coupled ordinary differential equations. This system of ordinary differential equations is addressed numerically. The graphical outcomes are scrutinized by utilizing the MATLAB software bvp4c function. The results revealed that the velocity profile decreases for the higher rotation parameter while increases for the escalated slip parameter. Furthermore, the fluid concentration and temperature are on the decline for higher surface catalyzed reaction and thermal relaxation parameters respectively.
Citation - WoS: 9
Citation - Scopus: 13
Positivity Preserving Interpolation by Using Rational Quartic Spline
(Amer inst Mathematical Sciences-aims, 2020) Karim, Samsul Ariffin Abdul; Othman, Mahmod; Saaban, Azizan; Ghaffar, Abdul; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Harim, Noor Adilla
In this study, a new scheme for positivity preserving interpolation is proposed by using C-1 rational quartic spline of (quartic/quadratic) with three parameters. The sufficient condition for the positivity rational quartic interpolant is derived on one parameter meanwhile the other two are free parameters for shape modification. These conditions will guarantee to provide positive interpolating curve everywhere. We tested the proposed positive preserving scheme with four positive data and compared the results with other established schemes. Based on the graphical and numerical results, we found that the proposed scheme is better than existing schemes, since it has extra free parameter to control the positive interpolating curve.
Citation - WoS: 4
Citation - Scopus: 5
Analytical Properties of the Hurwitz-Lerch Zeta Function
(Springer, 2020) Usman, Talha; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Nadeem, Raghib
In the present paper, we aim to extend the Hurwitz-Lerch zeta function Phi delta,sigma;gamma(xi ,s,upsilon ;p) involving the extension of the beta function (Choi et al. in Honam Math. J. 36(2):357-385, 2014). We also study the basic properties of this extended Hurwitz-Lerch zeta function which comprises various integral formulas, a derivative formula, the Mellin transform, and the generating relation. The fractional kinetic equation for an extended Hurwitz-Lerch zeta function is also obtained from an application point of view. Furthermore, we obtain certain interesting relations in the form of particular cases.
Citation - WoS: 16
Citation - Scopus: 20
Role of Cattaneo-Christov Heat Flux in an Mhd Micropolar Dusty Nanofluid Flow With Zero Mass Flux Condition
(Nature Portfolio, 2021) Gul, Hina; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Malik, M. Y.; Ramzan, Muhammad
This investigation aims to look at the thermal conductivity of dusty Micropolar nanoliquid with MHD and Cattaneo-Christov heat flux flow over an elongated sheet. The novelty of the envisioned mathematical model is augmented with the added impacts of the heat source/sink, chemical reaction with slip, convective heat, and zero mass flux boundary conditions. The salient feature of the existing problem is to discuss the whole scenario with liquid and dust phases. The graphical depiction is attained for arising pertinent parameters by using bvp4c a built-in MATLAB function. It is noticed that the thermal profile and velocity field increases for greater values of liquid particle interaction parameter in the case of the dust phase. An escalation in the thermal profile of both liquid and dust phases is noticed for the magnetic parameter. The rate of mass transfer amplifies for large estimates of the Schmidt number. The thickness of the boundary layer and the fluid velocity are decreased as the velocity slip parameter is augmented. In both dust and liquid phases, the thermal boundary layer thickness is lessened for growing estimates of thermal relaxation time. The attained results are verified when compared with a published result.
Citation - WoS: 25
Citation - Scopus: 23
Existence and Uniqueness of Solutions for Fractional Nonlinear Hybrid Impulsive System
(Wiley, 2022) Jarad, Fahd; Valliammal, Natarajan; Ravichandran, Chokkalingam; Nisar, Kottakkaran Sooppy; Gupta, Vidushi
The investigation of existence and uniqueness of impulsive dynamical fractional systems with quadratic perturbation of second type subject to nonlocal boundary conditions is presented and proved. By employing the fractional theory, Banach contraction technique, and Krasnoselskii's fixed point theorem, we derived some sufficient conditions to ensure the existence of our system. An example is offered to enhance the applicability of the results obtained.
Citation - WoS: 26
Citation - Scopus: 36
Lie Symmetry Analysis, Explicit Solutions and Conservation Laws of a Spatially Two-Dimensional Burgers-Huxley Equation
(Mdpi, 2020) Bano, Shahida; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Hussain, Amjad
In this paper, we investigate a spatially two-dimensional Burgers-Huxley equation that depicts the interaction between convection effects, diffusion transport, reaction gadget, nerve proliferation in neurophysics, as well as motion in liquid crystals. We have used the Lie symmetry method to study the vector fields, optimal systems of first order, symmetry reductions, and exact solutions. Furthermore, using the power series method, a set of series solutions are obtained. Finally, conservation laws are derived using optimal systems.
Citation - WoS: 22
Citation - Scopus: 25
New Approach on Controllability of Hilfer Fractional Derivatives With Nondense Domain
(Amer inst Mathematical Sciences-aims, 2022) Jothimani, Kasthurisamy; Ravichandran, Chokkalingam; Baleanu, Dumitru; Kumar, Devendra; Nisar, Kottakkaran Sooppy
This work picturizes the results on the controllability of the nondense Hilfer neutral fractional derivative (HNFD). The uniqueness and controllability of HNFD are discussed with Winch theorem and Banach contraction technique. In addition, a numerical approximation is given to deal with different criteria of our results.
A Note On (P, Q)-Analogue Type of Fubini Numbers and Polynomials
(American Institute of Mathematical Sciences, 2020) Khan, Waseem Ahmad; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru
In this paper, we introduce a new class of (p, q)-analogue type of Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we consider some relationships for (p, q)-Fubini polynomials associated with (p, q)-Bernoulli polynomials, (p, q)-Euler polynomials and (p, q)-Genocchi polynomials and (p, q)-Stirling numbers of the second kind.
Citation - WoS: 8
Citation - Scopus: 11
A Note on (P, Q)-Analogue Type of Fubini Numbers and Polynomials
(Amer inst Mathematical Sciences-aims, 2020) Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Khan, Waseem Ahmad
In this paper, we introduce a new class of (p, q)-analogue type of Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we consider some relationships for (p, q)-Fubini polynomials associated with (p, q)-Bernoulli polynomials, (p, q)-Euler polynomials and (p, q)-Genocchi polynomials and (p, q)-Stirling numbers of the second kind.
Citation - WoS: 12
Citation - Scopus: 15
On the Weighted Fractional Integral Inequalities for Chebyshev Functionals
(Springer, 2021) Nisar, Kottakkaran Sooppy; Khan, Sami Ullah; Baleanu, Dumitru; Vijayakumar, V.; Rahman, Gauhar
The goal of this present paper is to study some new inequalities for a class of differentiable functions connected with Chebyshev's functionals by utilizing a fractional generalized weighted fractional integral involving another function G in the kernel. Also, we present weighted fractional integral inequalities for the weighted and extended Chebyshev's functionals. One can easily investigate some new inequalities involving all other type weighted fractional integrals associated with Chebyshev's functionals with certain choices of omega(theta) and G(theta) as discussed in the literature. Furthermore, the obtained weighted fractional integral inequalities will cover the inequalities for all other type fractional integrals such as Katugampola fractional integrals, generalized Riemann-Liouville fractional integrals, conformable fractional integrals and Hadamard fractional integrals associated with Chebyshev's functionals with certain choices of omega(theta) and G(theta).
Citation - WoS: 37
Citation - Scopus: 39
Enhanced Heat Transfer in Moderately Ionized Liquid Due To Hybrid Mos2/Sio2 Nanofluids Exposed by Nonlinear Radiation: Stability Analysis
(Mdpi, 2020) Zaib, A.; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Khan, Umair
This study considers ethylene-glycol as a moderate ionized regular liquid whose rheological behavior can be analyzed through the relations of the Carreau stress-strain tensor. Hybrid nanoliquids are potent liquids that give better performance for heat transfer and the properties of thermo physical than regular heat transfer liquids (water, ethylene glycol, and oil) and nanoliquids by single nanomaterials. Here, a type of hybrid nanoliquid involving silicon oxide (SiO2) and Molybdenum disulfide (MoS2) nanoparticles with ethylene glycol as a base liquid are considered. In addition, the impact of nonlinear radiation along with Lorentz force is invoked. Similarity variables are utilized to acquire the numerical findings and their solutions for transmuting ordinary differential equations (ODEs). Using bvp4c from MATLAB, we can obtain these quantitative and numerical results of the converted nonlinear equations. The impacts of the pertinent constraints on the temperature distribution, velocity, Nusselt number, and skin friction are estimated. The outcomes indicate that the double-edged methods for the results originate from the precise values of the permeable parameters. Further, the critical values (S-c = 1.9699, 2.0700 and 2.2370) are enhanced due to the influence of the local Weissenberg number. This implies that the increasing value of the local Weissenberg number accelerate the boundary layer separation. Furthermore, a stability investigation is performed and confirms that the first solution is a physically reliable solution.
Citation - WoS: 53
Citation - Scopus: 72
On Beta-Time Fractional Biological Population Model With Abundant Solitary Wave Structures
(Elsevier, 2022) Nisar, Kottakkaran Sooppy; Ciancio, Armando; Ali, Khalid K.; Osman, M. S.; Cattani, Carlo; Baleanu, Dumitru; Azeem, M.
The ongoing study deals with various forms of solutions for the biological population model with a novel beta-time derivative operators. This model is very conducive to explain the enlargement of viruses, parasites and diseases. This configuration of the aforesaid classical scheme is scouted for its new solutions especially in soliton shape via two of the well known analytical strategies, namely: the extended Sinh-Gordon equation expansion method (EShGEEM) and the Expa function method. These soliton solutions suggest that these methods have widened the scope for generating solitary waves and other solutions of fractional differential equations. Different types of soliton solutions will be gained such as dark, bright and singular solitons solutions with certain conditions. Furthermore, the obtained results can also be used in describing the biological population model in some better way. The numerical solution for the model is obtained using the finite difference method. The numerical simulations of some selected results are also given through their physical explanations. To the best of our knowledge, No previous literature discussed this model through the application of the EShGEEM and the Expa function method and supported their new obtained results by numerical analysis. (c) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
Citation - WoS: 11
Citation - Scopus: 13
Family of Odd Point Non-Stationary Subdivision Schemes and Their Applications
(Springeropen, 2019) Ullah, Zafar; Bari, Mehwish; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Ghaffar, Abdul
The (2s-1)-point non-stationary binary subdivision schemes (SSs) for curve design are introduced for any integer s2. The Lagrange polynomials are used to construct a new family of schemes that can reproduce polynomials of degree (2s-2). The usefulness of the schemes is illustrated in the examples. Moreover, the new schemes are the non-stationary counterparts of the stationary schemes of (Daniel and Shunmugaraj in 3rd International Conference on Geometric Modeling and Imaging, pp.3-8, 2008; Hassan and Dodgson in Curve and Surface Fitting: Sant-Malo 2002, pp.199-208, 2003; Hormann and Sabin in Comput. Aided Geom. Des. 25:41-52, 2008; Mustafa et al. in Lobachevskii J. Math. 30(2):138-145, 2009; Siddiqi and Ahmad in Appl. Math. Lett. 20:707-711, 2007; Siddiqi and Rehan in Appl. Math. Comput. 216:970-982, 2010; Siddiqi and Rehan in Eur. J. Sci. Res. 32(4):553-561, 2009). Furthermore, it is concluded that the basic shapes in terms of limiting curves produced by the proposed schemes with fewer initial control points have less tendency to depart from their tangent as well as their osculating plane compared to the limiting curves produced by existing non-stationary subdivision schemes.
Citation - WoS: 86
Citation - Scopus: 120
Analysis and Dynamics of Fractional Order Mathematical Model of Covid-19 in Nigeria Using Atangana-Baleanu Operator
(Tech Science Press, 2021) Shaikh, Amjad S.; Ibrahim, Mohammed O.; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Khan, Ilyas; Abioye, Adesoye I.; Peter, Olumuyiwa J.
We propose a mathematical model of the coronavirus disease 2019 (COVID-19) to investigate the transmission and control mechanism of the disease in the community of Nigeria. Using stability theory of differential equations, the qualitative behavior of model is studied. The pandemic indicator represented by basic reproductive number R-0 is obtained from the largest eigenvalue of the next-generation matrix. Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease. Further, we examined this model by using Atangana-Baleanu fractional derivative operator and existence criteria of solution for the operator is established. We consider the data of reported infection cases from April 1, 2020, till April 30, 2020, and parameterized the model. We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations. The impacts of various biological parameters on transmission dynamics of COVID-19 is examined. These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease. In the end, the obtained results are demonstrated graphically to justify our theoretical findings.