Browsing by Author "Nisar, Kottakkaran Sooppy"

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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; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
A note on (p, q)-analogue type of Fubini numbers and polynomials
(2020) Khan, Waseem Ahmad; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 12
Citation - Scopus: 13
Al2o3 and Γal2o3 Nanomaterials Based Nanofluid Models With Surface Diffusion: Applications for Thermal Performance in Multiple Engineering Systems and Industries
(Tech Science Press, 2021) Khan, Umar; Ahmed, Naveed; Mohyud-Din, Syed Tauseef; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Nan, Adnan; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 85
Citation - Scopus: 116
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.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 113
Citation - Scopus: 138
Analysis of Differential Equations Involving Caputo-Fabrizio Fractional Operator and Its Applications To Reaction-Diffusion Equations
(Springer, 2019) Tassaddiq, Asifa; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Shaikh, Amjad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 29
Citation - Scopus: 33
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, 2020) Rasheed, Haroon Ur; Abbas, Tariq; Khan, Waris; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Khan, Zeeshan; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 13
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; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 4
Citation - Scopus: 5
Analytical Properties of the Hurwitz-Lerch Zeta Function
(Springer, 2020) Usman, Talha; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Nadeem, Raghib; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 6
Citation - Scopus: 11
Analytical Solution of System of Volterra Integral Equations Using Oham
(Hindawi Ltd, 2020) Nawaz, Rashid; Ahsan, Sumbal; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Akbar, Muhammad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 4
Citation - Scopus: 3
Approximate Solutions of Nonlinear Two-Dimensional Volterra Integral Equations
(Wiley, 2021) Nawaz, Rashid; Akbar, Muhammad; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Ahsan, Sumbal; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 30
Citation - Scopus: 32
Bounds of Generalized Proportional Fractional Integrals in General Form Via Convex Functions and Their Applications
(Mdpi, 2020) Jarad, Fahd; Nisar, Kottakkaran Sooppy; Rahman, Gauhar; Abdeljawad, Thabet; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, our objective is to apply a new approach to establish bounds of sums of left and right proportional fractional integrals of a general type and obtain some related inequalities. From the obtained results, we deduce some new inequalities for classical generalized proportional fractional integrals as corollaries. These inequalities have a connection with some known and existing inequalities which are mentioned in the literature. In addition, some applications of the main results are presented.
Citation - WoS: 66
Citation - Scopus: 64
Certain Inequalities Via Generalized Proportional Hadamard Fractional Integral Operators
(Springer, 2019) Jarad, Fahd; Khan, Aftab; Nisar, Kottakkaran Sooppy; Rahman, Gauhar; Abdeljawad, Thabet; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In the article, we introduce the generalized proportional Hadamard fractional integrals and establish several inequalities for convex functions in the framework of the defined class of fractional integrals. The given results are generalizations of some known results.
Citation - WoS: 10
Citation - Scopus: 10
Comparative Thermal Performance in Sio2-H2o and (mos2-Sio2) Over a Curved Stretching Semi-Infinite Region: a Numerical Investigation
(Tech Science Press, 2021) Khan, Umar; Wahab, Hafiz Abdul; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Ullah, Basharat; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The investigation of Thermal performance in nanofluids and hybrid nanofluids over a curved stretching infinite region strengthens its roots in engineering and industry. Therefore, the comparative thermal analysis in SiO2-H2O and (MoS2-SiO2)-H2O is conducted over curved stretching surface. The model is reduced in the dimensional version via similarity transformation and then treated numerically. The velocity and thermal behavior for both the fluids is decorated against the preeminent parameters. From the analysis, it is examined that the motion of under consideration fluids declines against Fr and lambda. The thermal performance enhances for higher volumetric fraction and lambda. Further, it is noticed that thermal performance prevailed in (MoS2-SiO2)-H2O throughout the analysis. Therefore, (MoS2-SiO2)-H2O is better for industrial and engineering uses where high heat transfer is required to accomplished different processes of production.
Citation - WoS: 16
Citation - Scopus: 20
Computable Solution of Fractional Kinetic Equations Using Mathieu-Type Series
(Springer, 2019) Khan, Nabiullah; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Khan, Owais; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The Mathieu series appeared in the study of elasticity of solid bodies in the work of Emile Leonard Mathieu. Since then numerous authors have studied various problems arising from the Mathieu series in several diverse ways. In this line, our aim is to study the solution of fractional kinetic equations involving generalized Mathieu-type series. The generality of this series will help us to deduce results related to a fractional kinetic equation involving another form of Mathieu series. To obtain the solution, we use the Laplace transform technique. Besides, a graphical representation is given to observe the behavior of the obtained solutions.
Citation - WoS: 2
Citation - Scopus: 4
Construction and Analysis of Unified 4-Point Interpolating Nonstationary Subdivision Surfaces
(Springer, 2021) Mustafa, Ghulam; Ghaffar, Abdul; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Bari, Mehwish; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Subdivision schemes (SSs) have been the heart of computer-aided geometric design almost from its origin, and several unifications of SSs have been established. SSs are commonly used in computer graphics, and several ways were discovered to connect smooth curves/surfaces generated by SSs to applied geometry. To construct the link between nonstationary SSs and applied geometry, in this paper, we unify the interpolating nonstationary subdivision scheme (INSS) with a tension control parameter, which is considered as a generalization of 4-point binary nonstationary SSs. The proposed scheme produces a limit surface having C1 smoothness. It generates circular images, spirals, or parts of conics, which are important requirements for practical applications in computer graphics and geometric modeling. We also establish the rules for arbitrary topology for extraordinary vertices (valence >= 3). The well-known subdivision Kobbelt scheme (Kobbelt in Comput. Graph. Forum 15(3):409-420, 1996) is a particular case. We can visualize the performance of the unified scheme by taking different values of the tension parameter. It provides an exact reproduction of parametric surfaces and is used in the processing of free-form surfaces in engineering.
Citation - WoS: 13
Citation - Scopus: 25
Construction and Application of Nine-Tic B-Spline Tensor Product Ss
(Mdpi, 2019) Ghaffar, Abdul; Iqbal, Mudassar; Bari, Mehwish; Hussain, Sardar Muhammad; Manzoor, Raheela; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we propose and analyze a tensor product of nine-tic B-spline subdivision scheme (SS) to reduce the execution time needed to compute the subdivision process of quad meshes. We discuss some essential features of the proposed SS such as continuity, polynomial generation, joint spectral radius, holder regularity and limit stencil. Some results of the SS using surface modeling with the help of computer programming are shown.
Citation - WoS: 19
Citation - Scopus: 24
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; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 16
Citation - Scopus: 22
Construction of New Cubic Bezier-Like Triangular Patches With Application in Scattered Data Interpolation
(Springer, 2020) Saaban, Azizan; Skala, Vaclav; Ghaffar, Abdul; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Karim, Samsul Ariffin Abdul; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper discusses the functional scattered data interpolation to interpolate the general scattered data. Compared with the previous works, we construct a new cubic Bezier-like triangular basis function controlled by three shape parameters. This is an advantage compared with the existing schemes since it gives more flexibility for the shape design in geometric modeling. By choosing some suitable value of the parameters, this new triangular basis is reduced to the cubic Ball and cubic Bezier triangular patches, respectively. In order to apply the proposed bases to general scattered data, firstly the data is triangulated using Delaunay triangulation. Then the sufficient condition for C-1 continuity using cubic precision method on each adjacent triangle is implemented. Finally, the interpolation scheme is constructed based on a convex combination between three local schemes of the cubic Bezier-like triangular patches. The detail comparison in terms of maximum error and coefficient of determination r(2) with some existing meshfree methods i.e. radial basis function (RBF) such as linear, thin plate spline (TPS), Gaussian, and multiquadric are presented. From graphical results, the proposed scheme gives more visually pleasing interpolating surfaces compared with all RBF methods. Based on error analysis, for all four functions, the proposed scheme is better than RBFs except for data from the third function. Overall, the proposed scheme gives r(2) value between 0.99920443 and 0.99999994. This is very good for surface fitting for a large scattered data set.
Citation - WoS: 24
Citation - Scopus: 29
Convective Effect on Magnetohydrodynamic (Mhd) Stagnation Point Flow of Casson Fluid Over a Vertical Exponentially Stretching/Shrinking Surface: Triple Solutions
(Mdpi, 2020) Omar, Zurni; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Lund, Liaquat Ali; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In the current study, the characteristics of heat transfer of a steady, two-dimensional, stagnation point, and magnetohydrodynamic (MHD) flow of shear thickening Casson fluid on an exponentially vertical shrinking/stretching surface are examined in attendance of convective boundary conditions. The impact of the suction parameter is also considered. The system of governing partial differential equations (PDEs) and boundary conditions is converted into ordinary differential equations (ODEs) with the suitable exponential similarity variables of transformations and then solved using the shooting method with the fourth order Runge-Kutta method. Similarity transformation is an important class of phenomena in which scale symmetry allows one to reduce the number of independent variables of the problem. It should be noted that solutions of the ODEs show the symmetrical behavior of the PDES for the profiles of velocity and temperature. Similarity solutions are obtained for the case of stretching/shrinking and suction parameters. It is revealed that there exist two ranges of the solutions in the specific ranges of the physical parameters, three solutions depend on the opposing flow case where stagnation point (A) should be equal to 0.1, two solutions exist when lambda(1)= 0where lambda(1)is a mixed convection parameter andA > 0.1, and a single solution exists when lambda(1)> 0. Moreover, the effects of numerous applied parameters on velocity, temperature distributions, skin friction, and local Nusselt number are examined and given through tables and graphs for both shrinking and stretching surfaces.
Citation - WoS: 49
Citation - Scopus: 61
Dual Similarity Solutions of Mhd Stagnation Point Flow of Casson Fluid With Effect of Thermal Radiation and Viscous Dissipation: Stability Analysis
(Nature Portfolio, 2020) Omar, Zurni; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Lund, Liaquat Ali; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, the rate of heat transfer of the steady MHD stagnation point flow of Casson fluid on the shrinking/stretching surface has been investigated with the effect of thermal radiation and viscous dissipation. The governing partial differential equations are first transformed into the ordinary (similarity) differential equations. The obtained system of equations is converted from boundary value problems (BVPs) to initial value problems (IVPs) with the help of the shooting method which then solved by the RK method with help of maple software. Furthermore, the three-stage Labatto III-A method is applied to perform stability analysis with the help of a bvp4c solver in MATLAB. Current outcomes contradict numerically with published results and found inastounding agreements. The results reveal that there exist dual solutions in both shrinking and stretching surfaces. Furthermore, the temperature increases when thermal radiation, Eckert number, and magnetic number are increased. Signs of the smallest eigenvalue reveal that only the first solution is stable and can be realizable physically.