Browsing by Author "Nisar, Kottakkaran Sooppy"

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Citation Count: Ghaffar, Abdul...et al. (2019). "A new class of 2m-point binary non-stationary subdivision schemes", Advances in Difference Equations, Vol. 2019, No. 1.
A new class of 2m-point binary non-stationary subdivision schemes
(Springer Open, 2019) Ghaffar, Abdul; Ullah, Zafar; Bari, Mehwish; Nisar, Kottakkaran Sooppy; Al-Qurashi, Maysaa M.; Baleanu, Dumitru; 56389
A new class of 2m-point non-stationary subdivision schemes (SSs) is presented, including some of their important properties, such as continuity, curvature, torsion monotonicity, and convexity preservation. The multivariate analysis of subdivision schemes is extended to a class of non-stationary schemes which are asymptotically equivalent to converging stationary or non-stationary schemes. A comparison between the proposed schemes, their stationary counterparts and some existing non-stationary schemes has been depicted through examples. It is observed that the proposed SSs give better approximation and more effective results.
Citation Count: Ghaffar, A...et al. (2019). "A New Class of 2Q-Point Nonstationary Subdivision Schemes and Their Applications",Mathematics, Vol. 7, No. 7.
A New Class of 2Q-Point Nonstationary Subdivision Schemes and Their Applications
(MDPI AG, 2019) Ghaffar, Abdul; Bari, Mehwish; Ullah, Zafar; Iqbal, Mudassar; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
The main objective of this study is to introduce a new class of 2q-point approximating nonstationary subdivision schemes (ANSSs) by applying Lagrange-like interpolant. The theory of asymptotic equivalence is applied to find the continuity of the ANSSs. These schemes can be nicely generalized to contain local shape parameters that allow the user to locally adjust the shape of the limit curve/surface. Moreover, many existing approximating stationary subdivision schemes (ASSSs) can be obtained as nonstationary counterparts of the proposed ANSSs
Citation Count: Rashid, Saima...et al. (2020). "A New Dynamic Scheme via Fractional Operators on Time Scale", Frontiers in Physics, Vol. 8.
A New Dynamic Scheme via Fractional Operators on Time Scale
(2020) Rashid, Saima; Noor, Muhammad Aslam; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Rahman, Gauhar; 56389
The present work investigates the applicability and effectiveness of the generalized Riemann-Liouville fractional integral operator integral method to obtain new Minkowski, Gruss type and several other associated dynamic variants on an arbitrary time scale, which are communicated as a combination of delta and fractional integrals. These inequalities extend some dynamic variants on time scales, and tie together and expand some integral inequalities. The present method is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractional differential equations applied in mathematical physics.
Citation Count: Khan, Waseem Ahmad; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru (2020). "A note on (p, q)-analogue type of Fubini numbers and polynomials", AIMS Mathematics, Vol. 5, No. 3, pp. 2743-2757.
A note on (p, q)-analogue type of Fubini numbers and polynomials
(2020) Khan, Waseem Ahmad; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
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 Count: Khan, W.A.; Nisar, K.S.; Baleanu, D. (2020). "A Note On (P, Q)-Analogue Type of Fubini Numbers and Polynomials", Aims Mathematics, Vol. 5, No. 3, pp. 2743-2757.
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; 56389
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 Count: Khan, Waseem Ahmad; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru (2020). "A note on (p, q)-analogue type of Fubini numbers and polynomials", AIMS Mathematics, Vol. 5, No. 3, pp. 2743-2757.
A note on (p, q)-analogue type of Fubini numbers and polynomials
(2020) Khan, Waseem Ahmad; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
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 Count: Ghaffar, Abdul...et al. (2020). "A novel analytical technique to obtain the solitary solutions for nonlinear evolution equation of fractional order", Advances in Difference Equations, Vol. 2020, No. 1.
A novel analytical technique to obtain the solitary solutions for nonlinear evolution equation of fractional order
(2020) Ghaffar, Abdul; Ali, Ayyaz; Ahmed, Sarfaraz; Akram, Saima; Junjua, Moin-ud-Din; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; 56389
We investigate some solitary wave results of time fractional evolution equations. By employing the extended rationalexp((-psi '/psi)(eta))-expansion method, a few different results including kink, singular-kink, multiple soliton, and periodic wave solutions are formally generated. It is worth mentioning that the solutions obtained are more general with more parameters. The exact solutions are constructed in the form of exponential, trigonometric, rational, and hyperbolic functions. With the choice of proper values of parameters, graphs to some of the obtained solutions are drawn. On comparing some special cases, our solutions are in good agreement with the results published previously and the remaining are new.
Citation Count: Khan, U...et al. (2020). "A Novel Hybrid Model for Cu-Al2O3/H2O Nanofluid Flow and Heat Transfer in Convergent/Divergent Channels", Energies, Vol. 13, No. 7.
A Novel Hybrid Model for Cu-Al2O3/H2O Nanofluid Flow and Heat Transfer in Convergent/Divergent Channels
(MDPI AG, 2020) Khan, Umar; Adnan, A.; Ahmed, Naveed; Mohyud-Din, S. T.; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Khan, I.; 56389
In the present study, our aim is to present a novel model for the flow of hybrid nanofluids in oblique channels. Copper and aluminum oxide have been used to obtain a novel hybrid nanofluid. The equations that govern the flow of hybrid nanofluids have been transformed to a set of nonlinear equations with the implementation of self-similar variables. The resulting system is treated numerically by using coupled shooting and Runge-Kutta (R-K) scheme. The behavior of velocity and temperature is examined by altering the flow parameters. The cases for narrowing (convergent) and opening (divergent) channels are discussed, and the influence of various parameters on Nusselt number is also presented. To indicate the reliability of the study, a comparison is made that confirms the accuracy of the study presented.
Citation Count: Shahzad, Aamir...et al. (2020). "A Novel Numerical Algorithm to Estimate the Subdivision Depth of Binary Subdivision Schemes", Symmetry-Basel, vol. 12, No. 1.
A Novel Numerical Algorithm to Estimate the Subdivision Depth of Binary Subdivision Schemes
(2020) Shahzad, Aamir; Khan, Faheem; Ghaffar, Abdul; Mustafa, Ghulam; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
Subdivision schemes are extensively used in scientific and practical applications to produce continuous geometrical shapes in an iterative manner. We construct a numerical algorithm to estimate subdivision depth between the limit curves/surfaces and their control polygons after k-fold subdivisions. In this paper, the proposed numerical algorithm for subdivision depths of binary subdivision curves and surfaces are obtained after some modification of the results given by Mustafa et al in 2006. This algorithm is very useful for implementation of the parametrization.
Citation Count: Ashraf, Pakeeza...et al. (2021). "A shape-preserving variant of Lane-Riesenfeld algorithm", AIMS Mathematics, Vol. 6, No. 3, pp. 2152-2170.
A shape-preserving variant of Lane-Riesenfeld algorithm
(2021) Ashraf, Pakeeza; Mustafa, Ghulam; Khan, Husna A.; Baleanu, Dumitru; Ghaffar, Abdul; Nisar, Kottakkaran Sooppy; 56389
This paper introduces a family of shape-preserving binary approximating subdivision schemes by applying a shape-preserving variant on the Lane-Riesenfeld algorithm. Using the symbols of subdivision schemes, we determine convergence and smoothness, Holder continuity, and support size of the limit curves. Furthermore, these schemes produce monotonic and convex curves under the certain conditions imposed on the initial data.
Citation Count: Mustafa, Ghulam...et al. (2020). "A subdivision-based approach for singularly perturbed boundary value problem", Advances in Difference Equations, Vol. 2020, No. 1.
A subdivision-based approach for singularly perturbed boundary value problem
(2020) Mustafa, Ghulam; Ejaz, Syeda Tehmina; Baleanu, Dumitru; Ghaffar, Abdul; Nisar, Kottakkaran Sooppy; 56389
A numerical approach for solving second order singularly perturbed boundary value problems (SPBVPs) is introduced in this paper. This approach is based on the basis function of a 6-point interpolatory subdivision scheme. The numerical results along with the convergence, comparison and error estimation of the proposed approach are also presented.
Citation Count: Nan, Adnan...et al. (2021). "Al2O3 and gamma Al2O3 Nanomaterials Based Nanofluid Models with Surface Diffusion: Applications for Thermal Performance in Multiple Engineering Systems and Industries", CMC-Computers Materials & Continua, Vol. 66, No. 2, pp. 1563-1576.
Al2O3 and gamma Al2O3 Nanomaterials Based Nanofluid Models with Surface Diffusion: Applications for Thermal Performance in Multiple Engineering Systems and Industries
(2021) Nan, Adnan; Khan, Umar; Ahmed, Naveed; Mohyud-Din, Syed Tausee; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; 56389
Thermal transport investigation in colloidal suspensions is taking a significant research direction. The applications of these fluids are found in various industries, engineering, aerodynamics, mechanical engineering and medical sciences etc. A huge amount of thermal transport is essential in the operation of various industrial production processes. It is a fact that conventional liquids have lower thermal transport characteristics as compared to colloidal suspensions. The colloidal suspensions have high thermal performance due to the thermophysical attributes of the nanoparticles and the host liquid. Therefore, researchers focused on the analysis of the heat transport in nanofluids under diverse circumstances. As such, the colloidal analysis of H2O composed by gamma Al2O3 and Al2O3 is conducted over an elastic cylinder. The governing flow models of gamma Al2O3/H2O and Al2O3/H2O is reduced in the dimensionless form by adopting the described similarity transforms. The colloidal models are handled by implementing the suitable numerical technique and provided the results for the velocity, temperature and local thermal performance rate against the multiple flow parameters. From the presented results, it is shown that the velocity of Al(2)O3-H2O increases promptly against a high Reynolds number and it decreases for high-volume fraction. The significant contribution of the volumetric fraction is examined for thermal enhancement of nanofluids. The temperature of Al2O3-H2O and gamma Al2O3-H-2O significantly increases against a higher phi. Most importantly, the analysis shows that gamma Al2O3-H2O has a high local thermal performance rate compared to Al2O3-H2O. Therefore, it is concluded that gamma Al2O3-H2O is a better heat transfer fluid and is suitable for industrial and technological uses.
Citation Count: Ali, Ihteram...et al. (2021). "An efficient numerical scheme based on Lucas polynomials for the study of multidimensional Burgers-type equations", Advances in Difference Equations, Vol. 2021, No. 1.
An efficient numerical scheme based on Lucas polynomials for the study of multidimensional Burgers-type equations
(2021) Ali, Ihteram; Haq, Sirajul; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
We propose a polynomial-based numerical scheme for solving some important nonlinear partial differential equations (PDEs). In the proposed technique, the temporal part is discretized by finite difference method together with theta-weighted scheme. Then, for the approximation of spatial part of unknown function and its spatial derivatives, we use a mixed approach based on Lucas and Fibonacci polynomials. With the help of these approximations, we transform the nonlinear partial differential equation to a system of algebraic equations, which can be easily handled. We test the performance of the method on the generalized Burgers-Huxley and Burgers-Fisher equations, and one- and two-dimensional coupled Burgers equations. To compare the efficiency and accuracy of the proposed scheme, we computed L-infinity, L-2, and root mean square (RMS) error norms. Computations validate that the proposed method produces better results than other numerical methods. We also discussed and confirmed the stability of the technique.
Citation Count: Peter, Olumuyiwa J...et al. (2021). "Analysis and Dynamics of Fractional Order Mathematical Model of COVID-19 in Nigeria Using Atangana-Baleanu Operator", CMC-Computers Materials & Continua, Vol. 66, No. 2.
Analysis and Dynamics of Fractional Order Mathematical Model of COVID-19 in Nigeria Using Atangana-Baleanu Operator
(2021) Peter, Olumuyiwa J.; Shaikh, Amjad S.; Ibrahim, Mohammed O.; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Khan, Ilyas; Abioye, Adesoye I.; 56389
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.
Citation Count: Shaikh, Amjad...et al. (2019). Analysis of differential equations involving Caputo-Fabrizio fractional operator and its applications to reaction-diffusion equations", Advances in Difference Equations.
Analysis of differential equations involving Caputo-Fabrizio fractional operator and its applications to reaction-diffusion equations
(Springer Open, 2019) Shaikh, Amjad; Tassaddiq, Asifa; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
This manuscript deals with fractional differential equations including Caputo-Fabrizio differential operator. The conditions for existence and uniqueness of solutions of fractional initial value problems is established using fixed point theorem and contraction principle, respectively. As an application, the iterative Laplace transform method (ILTM) is used to get an approximate solutions for nonlinear fractional reaction-diffusion equations, namely the Fitzhugh-Nagumo equation and the Fisher equation in the Caputo-Fabrizio sense. The obtained approximate solutions are compared with other available solutions from existing methods by using graphical representations and numerical computations. The results reveal that the proposed method is most suitable in terms of computational cost efficiency, and accuracy which can be applied to find solutions of nonlinear fractional reaction-diffusion equations.
Citation Count: Khan, Z...et al. (2020). "Analysis of Eyring–Powell Fluid Flow Used As A Coating Material for Wire With Variable Viscosity Effect Along With Thermal Radiation and Joule Heating", Crystals, Vol. 10, No. 3.
Analysis of Eyring–Powell Fluid Flow Used As A Coating Material for Wire With Variable Viscosity Effect Along With Thermal Radiation and Joule Heating
(MDPI AG, 2020) Khan, Zeeshan; Rasheed, Haroon Ur; Abbas, Tariq; Khan, Waris; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; 56389
This article examines a wire coating technique that considers how viscoelastic Eyring– Powell fluid is studied with magnetohydrodynamic (MHD) flow, thermal transfer, and Joule heating effects. Temperature-dependent variable and flexible viscosity models are considered. The interface boundary layer equalities which describe flux and thermal convective phenomena are evaluated using a dominant numerical technique—the so-called Runge–Kutta 4th-order method. A permeable matrix which behaves like a dielectric to avoid heat dissipation is taken into account and is the distinguishing aspect of this article. The effect of thermal generation is also explained, as it controls power. The effects of various parameters, such as non-Newtonian fluid, magnetic field, permeability, and heat source/sink, on wire coating processes are investigated through graphs and explained in detail. For the sake of validity, numerical techniques are compared with a semi-numerical technique (HAM) and BVPh2, and an outstanding agreement is found.
Citation Count: Ashraf, P...et al. (2020). "Analysis of Homotopy Perturbation Method for Solving Fractional Order Differential Equations",Mathematics, Vol. 8, No. 3.
Analysis of Geometric Properties of Ternary Four-Point Rational Interpolating Subdivision Scheme
(MDPI AG, 2020) Pakeeza, Ashraf; Bushra, Nawaz,; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Ghaffar, Abdul; Ahmed Khan, Muhammad Aqeel; Akram, Saima; 56389
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 Count: Nadeem, Raghib...et al. (2020). "Analytical properties of the Hurwitz-Lerch zeta function", Advances in Difference Equations, Vol. 2020, No. 1.
Analytical properties of the Hurwitz-Lerch zeta function
(2020) Nadeem, Raghib; Usman, Talha; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
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 Count: Akbar, Muhammad...et al. (2020). "Analytical Solution of System of Volterra Integral Equations Using OHAM", Journal of Mathematics, Vol. 2020.
Analytical Solution of System of Volterra Integral Equations Using OHAM
(2020) Akbar, Muhammad; Nawaz, Rashid; Ahsan, Sumbal; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; 56389
In this work, a reliable technique is used for the solution of a system of Volterra integral equations (VIEs), called optimal homotopy asymptotic method (OHAM). The proposed technique is successfully applied for the solution of different problems, and comparison is made with the relaxed Monto Carlo method (RMCM) and hat basis function method (HBFM). The comparisons show that the present technique is more suitable and reliable for the solution of a system of VIEs. The presented technique uses auxiliary function containing auxiliary constants, which control the convergence. Moreover, OHAM does not require discretization like other numerical methods and is also free from small or large parameter.
Citation Count: Ahsan, Sumbal...et al. (2021). "Approximate solutions of nonlinear two-dimensional Volterra integral equations", Mathematical Methods in the Applied Sciences, Vol. 44, No. 7, pp. 5548-5559.
Approximate solutions of nonlinear two-dimensional Volterra integral equations
(2021) Ahsan, Sumbal; Nawaz, Rashid; Akbar, Muhammad; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
The present work is concerned with examining the Optimal Homotopy Asymptotic Method (OHAM) for linear and nonlinear two-dimensional Volterra integral equations (2D-VIEs). The result obtained by the suggested method for linear 2D-VIEs is compared with the differential transform method, Bernstein polynomial method, and piecewise block-plus method and result of the proposed method for nonlinear 2D-VIEs is compared with 2D differential transform method. The proposed method provides us with efficient and more accurate solutions compared to the other existing methods in the literature.