Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Citation - WoS: 9
Citation - Scopus: 21
Study of Implicit Type Coupled System of Non-Integer Order Differential Equations With Antiperiodic Boundary Conditions
(Wiley, 2019) Shah, Kamal; Khan, Rahmat Ali; Baleanu, Dumitru; Samina
In this paper, the first purpose is to study existence and uniqueness of solutions to a system of implicit fractional differential equations (IFDEs) equipped with antiperiodic boundary conditions (BCs). To obtain the mentioned results, we use Schauder's and Banach fixed point theorem. The second purpose is discussing the Ulam-Hyers (UH) and generalized Ulam-Hyers (GUH) stabilities for the respective solutions. An example is provided to illustrate the established results.
Citation - WoS: 86
Citation - Scopus: 82
On Nonautonomous Complex Wave Solutions Described by the Coupled Schrodinger-Boussinesq Equation With Variable-Coefficients
(Springer, 2018) Machado, J. A. T.; Baleanu, Dumitru; Osman, M. S.
This paper investigates the coupled Schrodinger-Boussinesq equation with variable-coefficients using the unified method. New nonautonomous complex wave solutions are obtained and classified into two categories, namely polynomial function and rational function solutions. For the polynomial functions emerge the complex solitary, complex soliton and complex elliptic wave solutions, while for the rational function are observed complex periodic rational and complex hyperbolic rational wave solutions. The physical insight and the dynamical behavior of the solutions describing the wave propagation in laser or plasma physics are discussed and analysed for different choices of the arbitrary functions in the solutions.
Citation - WoS: 7
Citation - Scopus: 9
The Investigation of Fe3o4 Atomic Aggregation in a Nanochannel in the Presence of Magnetic Field: Effects of Nanoparticles Distance Center of Mass, Temperature and Total Energy Via Molecular Dynamics Approach
(Elsevier, 2022) Fagiry, Moram A.; Sajadi, S. Mohammad; Almasri, Radwan A.; Karimipour, Arash; Li, Zhixiong; Ghaemi, Ferial; Liu, Xinglong
The computational procedure was utilized to explain the size effect of Fe3O4 nanoparticles on atomic behavior and phenomena of nanoparticles accumulation in nanochannel of ideal platinum (Pt) and the external magnetic field. Argon (Ar) atoms were considered as the base liquid, and the molecular dynamics procedure was utilized in this investigation. We utilized the Lennard-Jones potential to interact between the particles, whereas the nanochannel and nanoparticles structures were simulated. To compute the atomic manner, the quantities of nanoparticles distance center of mass, and the aggregation duration were presented. The outcomes implied that the nanoparticles size had a significant role in the accumulation. As the nanoparticles' size increased, the accumulation time of nanoparticles reached to 1.29 ns. Also, the outer magnetic field could severly postpone this event. (C) 2021 Published by Elsevier B.V.
Citation - WoS: 119
Citation - Scopus: 138
New Aspects of Fractional Biswas-Milovic Model With Mittag-Leffler Law
(Edp Sciences S A, 2019) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev
This article deals with a fractional extension of Biswas-Milovic (BM) model having Kerr and parabolic law nonlinearities. The BM model plays a key role in describing the long-distance optical communications. The fractional homotopy analysis transform technique (FHATM) is applied to examine the BM equation involving Atangana-Baleanu (AB) derivative of fractional order. The FHATM is constructed by using homotopy analysis technique, Laplace transform algorithm and homotopy polynomials. The numerical simulation work is performed with the aid of maple software package. In order to demonstrate the effects of order of AB operator, variables and parameters on the displacement, the results are shown graphically. The outcomes of the present investigation are very encouraging and show that the AB fractional operator is very useful in mathematical modelling of natural phenomena.
Citation - WoS: 143
Citation - Scopus: 157
Semi-Analytical Study of Pine Wilt Disease Model With Convex Rate Under Caputo-Febrizio Fractional Order Derivative
(Pergamon-elsevier Science Ltd, 2020) Jarad, Fahd; Abdeljawad, Thabet; Shah, Kamal; Alqudah, Manar A.
In this paper, we present semi-analytical solution to Pine Wilt disease (PWD) model under the CaputoFabrizio fractional derivative (CFFD). For the proposed solution, we utilize Laplace transform coupled with Adomian decomposition method abbreviated as (LADM). The concerned method is a powerful tool to obtain semi-analytical solution for such type of nonlinear differential equations of fractional order (FODEs) involving non-singular kernel. Furthermore, we give some results for the existence of solution to the proposed model and present numerical results to verify the established analysis. (C) 2020 Elsevier Ltd. All rights reserved.
Citation - WoS: 29
Citation - Scopus: 36
A Tau-Like Numerical Method for Solving Fractional Delay Integro-Differential Equations
(Elsevier, 2020) Ostadzad, M. H.; Baleanu, D.; Shahmorad, Sedaghat
In this paper, an operational matrix formulation of the Tau method is herein discussed to solve a class of delay fractional integrodifferential equations. The approximate solution is sought by using a suitable matrix representation of fractional and delay integrals. An error bound is herein for the first time discussed. Numerical examples show the effectiveness of the method. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.
Citation - WoS: 178
Citation - Scopus: 189
On Fractional Calculus with General Analytic Kernels
(Elsevier Science Inc, 2019) Fernandez, Arran; Ozarslan, Mehmet Ali; Baleanu, Dumitru
Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel functions. We demonstrate, under some assumptions, how all of these modifications can be considered as special cases of a single, unifying, model of fractional calculus. We provide a fundamental connection with classical fractional calculus by writing these general fractional operators in terms of the original Riemann-Liouville fractional integral operator. We also consider inversion properties of the new operators, prove analogues of the Leibniz and chain rules in this model of fractional calculus, and solve some fractional differential equations using the new operators. (C) 2019 Elsevier Inc. All rights reserved.
On Hardy-Hilbert Inequalities With Α-Fractional Derivatives
(Amer inst Mathematical Sciences-aims, 2023) Hassanein, Wael S.; Elsayed, Marwa Sh.; Baleanu, Dumitru; El-Deeb, Ahmed A.; Ahmed, Marwa M.
In the current manuscript, new alpha delta dynamic Hardy-Hilbert inequalities on time scales are discussed. These inequalities combine and expand a number of continuous inequalities and their corresponding discrete analogues in the literature. We shall illustrate our results using Holder's inequality on time scales and a few algebraic inequalities.
Optical solitons to the (n+1)-dimensional nonlinear Schrodinger's equation with Kerr law and power law nonlinearities using two integration schemes
(2019) İnç, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Bayram, Mustafa; Baleanu, Dumitru
In this study, two integration techniques are employed to reach optical solitons to the (n + 1)-dimensional nonlinear Schrodinger's equation ((n + 1)-NLSE) with Kerr and power laws nonlinearities. These are the undetermined coefficient and Bernoulli sub-ODE methods. We acquired bright, dark, and periodic singular soliton solutions. The necessary conditions for the existence of these solitons are presented.
Citation - WoS: 87
Citation - Scopus: 96
On Electromagnetic Field in Fractional Space
(Pergamon-elsevier Science Ltd, 2010) Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Baleanu, Dumitru
Laplacian equation in fractional space describes complex phenomena of physics. With this view, potential of charge distribution in fractional space is derived using Gegenbauer polynomials. Multipoles and magnetic field of charges in fractional space have been obtained. (C) 2008 Elsevier Ltd. All rights reserved.
Citation - WoS: 23
Citation - Scopus: 26
New Newton's Type Estimates Pertaining To Local Fractional Integral Via Generalized P-Convexity With Applications
(World Scientific Publ Co Pte Ltd, 2021) Rashid, Saima; Hammouch, Zakia; Baleanu, Dumitru; Chu, Yu-ming; LI, Yong-min
This paper aims to investigate the notion of p-convex functions on fractal sets Double-struck capital R-alpha(0 < alpha <= 1). Based on these novel ideas, we derived an auxiliary result depend on a three-step quadratic kernel by employing generalized p-convexity. Take into account the local fractal identity, we established novel Newton's type variants for the local differentiable functions. Several special cases are apprehended in the light of generalized convex functions and generalized harmonically convex functions. This novel strategy captures several existing results in the relative literature. Application is obtained in cumulative distribution function and generalized special weighted means to confirm the relevance and computational effectiveness of the considered method. Finally, we supposed that the consequences of this paper can stimulate those who are interested in fractal analysis.
Citation - WoS: 51
Citation - Scopus: 60
Lie Symmetry Analysis and Explicit Solutions for the Time Fractional Generalized Burgers-Huxley Equation
(Springer, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, Mustafa
In this work, we study the time fractional generalized Burgers-Huxley equation with Riemann-Liouville derivative via Lie symmetry analysis and power series expansion method. We transform the governing equation to nonlinear ordinary differential equation of fractional order using its Lie point symmetries. In the reduced equation, the derivative is in Erdelyi-Kober sense. We apply power series technique to derive explicit solutions for the reduced equation. The convergence of the obtained power series solutions are also derived. Some interesting Figures for the obtained solutions are presented.
Citation - WoS: 89
Citation - Scopus: 104
Hybrid Nanofluid on Mixed Convective Radiative Flow From an Irregular Variably Thick Moving Surface With Convex and Concave Effects
(Elsevier, 2020) Shafiq, Anum; Zaib, A.; Baleanu, Dumitru; Khan, Umair
The analysis explores the significance of thermal radiation on mixed convective boundary layer flow of a hybrid (SiO2-MoS2/H2O) nanofluid. The permeability of the stretched/shrinking surface is allowing the wall fluid suction, whereas radiation phenomenon is also incorporated in the presence of thermal convection. The combination of SiO2 nanoparticles and MoS2/H2O nanofluid are being modeled using the analytical nanofluid hybrid model in the present work. The hybrid nanofluid governing equations are transformed utilizing the similarity transformation technique. The transformed boundary value problem, then solved by bvp4c technique in MATLAB software. For specified values of various parameters the numerical results are obtained. The findings indicate dual solutions, up to some amount of stretching/shrinking parameter. The suction parameter decelerates the friction factor and accelerates the heat transfer rate. Also, the tem-perature augments due to the radiation and nanoparticles volume fraction in both solutions, whereas the velocity declines due to nanoparticles volume fraction.
Citation - WoS: 25
Citation - Scopus: 29
Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid With Newtonian Heating: Prabhakar Fractional Derivative Approach
(Mdpi, 2022) Jarad, Fahd; Riaz, Muhammad Bilal; Shah, Zaheer Hussain; Rehman, Aziz Ur
In this article, the effects of Newtonian heating along with wall slip condition on temperature is critically examined on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer Maxwell fluid near an infinitely vertical plate under constant concentration. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on a newly introduced Prabhakar fractional operator with generalized Fourier's law and Fick's law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration, and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as alpha, Pr, beta, Sc, Gr, gamma, and Gm are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical Maxwell model, classical Newtonian model, and fractional Newtonian model are recovered from Prabhakar fractional Maxwell fluid. Moreover, we compare the results between Maxwell and Newtonian fluids for both fractional and classical cases with and without slip conditions, showing that the movement of the Maxwell fluid is faster than viscous fluid. Additionally, it is visualized that both classical Maxwell and viscous fluid have relatively higher velocity as compared to fractional Maxwell and viscous fluid.
Citation - WoS: 12
Citation - Scopus: 13
A Novel Time Efficient Structure-Preserving Splitting Method for the Solution of Two-Dimensional Reaction-Diffusion Systems
(Springer, 2020) Korkmaz, Alper; Rafiq, M.; Baleanu, Dumitru; Alshomrani, Ali Saleh; Rehman, M. A.; Iqbal, M. S.; Ahmed, Nauman
In this article, the first part is concerned with the important questions related to the existence and uniqueness of solutions for nonlinear reaction-diffusion systems. Secondly, an efficient positivity-preserving operator splitting nonstandard finite difference scheme (NSFD) is designed for such a class of systems. The presented formulation is unconditionally stable as well as implicit in nature and even time efficient. The proposed NSFD operator splitting technique also preserves all the important properties possessed by continuous systems like positivity, convergence to the fixed points of the system, and boundedness. The proposed algorithm is implicit in nature but more efficient in time than the extensively used Euler method.
Citation - WoS: 9
Citation - Scopus: 14
Finite Element Least Square Technique for Newtonian Fluid Flow Through a Semicircular Cylinder of Recirculating Region Via Comsol Multiphysics
(Hindawi Ltd, 2020) Memon, Abid A.; Memon, M. Asif; Bhatti, Kaleemullah; Shaikh, Gul M.; Baleanu, Dumitru; Alhussain, Ziyad A.; Khan, Ilyas
This article aims to study Newtonian fluid flow modeling and simulation through a rectangular channel embedded in a semicircular cylinder with the range of Reynolds number from 100 to 1500. The fluid is considered as laminar and Newtonian, and the problem is time independent. A numerical procedure of finite element's least Square technique is implemented through COMSOL multiphysics 5.4. The problem is validated through asymptotic solution governed through the screen boundary condition. The vortex length of the recirculating region formed at the back of the cylinder and orientation of velocity field and pressure will be discussed by three horizontal and four vertical lines along the recirculating region in terms of Reynolds number. It was found that the two vortices of unequal size have appeared and the lengths of these vortices are increased with the increase Reynolds number. Also, the empirical equations through the linear regression procedure were determined for those vortices. The orientation of the velocity magnitude as well as pressure along the lines passing through the center of upper and lower vortices are the same.
Citation - WoS: 37
Citation - Scopus: 41
New Solitary Wave Solutions and Stability Analysis of the Benney-Luke and the Phi-4 Equations in Mathematical Physics
(Amer inst Mathematical Sciences-aims, 2019) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Ghanbari, Behzad
In this paper, we present new solitary wave solutions for the Benney-Luke equation (BLE) and Phi-4 equation (PE). The new generalized rational function method (GERFM) is used to reach such solutions. Moreover, the stability for the governing equations is investigated via the aspect of linear stability analysis. It is proved that, both the governing equations are stable. We can also solve other nonlinear system of PDEs which are involve in mathematical physics and many other branches of physical sciences with the help of this new method.
Citation - WoS: 6
Citation - Scopus: 7
Fractional Spectral Differentiation Matrices Based on Legendre Approximation
(Springeropen, 2020) Baleanu, Dumitru; Ghorbani, Asghar
A simple scheme is proposed for computing NxN spectral differentiation matrices of fractional order alpha for the case of Legendre approximation. The algorithm derived here is based upon a homogeneous three-term recurrence relation and is numerically stable. The matrices are then applied to numerically differentiate.
Citation - WoS: 2
Citation - Scopus: 2
Hamiltonian Formulation of Singular Lagrangians on Time Scales
(Iop Publishing Ltd, 2008) Jarad, Fahd; Baleanu, Dumitru; Abdeljawad, Thabet
The Hamiltonian formulation of Lagrangian on time scale is investigated and the equivalence of Hamilton and Euler-Lagrange equations is obtained. The role of Lagrange multipliers is discussed.
Citation - WoS: 12
Citation - Scopus: 12
A Kamenev-Type Oscillation Result for a Linear (1+α)-Order Fractional Differential Equation
(Elsevier Science inc, 2015) Mustafa, Octavian G.; O'Regan, Donal; Baleanu, Dumitru
We investigate the eventual sign changing for the solutions of the linear equation (x((alpha)))' + q(t)x = t >= 0, when the functional coefficient q satisfies the Kamenev-type restriction lim sup 1/t epsilon integral(t)(to) (t - s)epsilon q(s)ds = +infinity for some epsilon > 2; t(0) > 0. The operator x((alpha)) is the Caputo differential operator and alpha is an element of (0, 1). (C) 2015 Elsevier Inc. All rights reserved.

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