Baleanu, Dumitru

Baleanu, Dumitru

Job Title

Dr. Öğr. Üyesi

Email Address

dumitru@cankaya.edu.tr

Main Affiliation

Matematik Bölümü

Status

Former Staff

Full item page

Scholarly Output

2199

Articles

4130

Citation Count

0

Supervised Theses

0 Scholarly Output Search Results

Now showing 1 - 10 of 14

New spectral techniques for systems of fractional differential equations using fractional-order generalized laguerre orthogonal functions
(Walter De Gruyter GMBH, 2014) Baleanu, Dumitru; Alhamed, Yahia A.; Baleanu, Dumitru; Al-Zahrani, A. A.; 56389
Fractional-order generalized Laguerre functions (FGLFs) are proposed depends on the definition of generalized Laguerre polynomials. In addition, we derive a new formula expressing explicitly any Caputo fractional-order derivatives of FGLFs in terms of FGLFs themselves. We also propose a fractional-order generalized Laguerre tau technique in conjunction with the derived fractional-order derivative formula of FGLFs for solving Caputo type fractional differential equations (FDEs) of order nu (0 < nu < 1). The fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order nu. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on FGLFs and compare them with other methods. Several numerical example are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques.
A Novel Analytical Technique of the Fractional Bagley-Torvik Equations for Motion of a Rigid Plate in Newtonian Fluids
(2020) Baleanu, Dumitru; Ramadan, Mohamed A.; Baleanu, Dumitru; Moatimid, Galal M.; 56389
The current paper is concerned with a modified Homotopy perturbation technique. This modification allows achieving an exact solution of an initial value problem of the fractional differential equation. The approach is powerful, effective, and promising in analyzing some classes of fractional differential equations for heat conduction problems and other dynamical systems. To crystallize the new approach, some illustrated examples are introduced.
Exploration of Aluminum and Titanium Alloys in the Stream-Wise and Secondary Flow Directions Comprising the Significant Impacts of Magnetohydrodynamic and Hybrid Nanofluid
(2020) Baleanu, Dumitru; Khan, Umair; Zaib, Aurang; Khan, Ilyas; Baleanu, Dumitru; 56389
This exploration examines the nonlinear effect of radiation on magnet flow consisting of hybrid alloy nanoparticles in the way of stream-wise and cross flow. Many experimental, as well as theoretical explorations, demonstrated that the thermal conductivity of the regular liquid increases by up to 15 to 40% when nanomaterials are mixed with the regular liquid. This change of the thermal conductivity of the nanoliquid depends on the various characteristics of the mixed nanomaterials like the size of the nanoparticles, the agglomeration of the particles, the volume fraction, etc. Researchers have used numerous nanoparticles. However, we selected water-based aluminum alloy (AA7075) and titanium alloy (Ti6Al4V) hybrid nanomaterials. This condition was mathematically modeled by capturing the Soret and Dufour impacts. The similarity method was exercised to change the partial differential equations (PDEs) into nonlinear ordinary differential equations (ODEs). Such nonlinear ODEs were worked out numerically via the bvp4c solver. The influences of varying the parameters on the concentration, temperature, and velocity area and the accompanying engineering quantities such as friction factor, mass, and heat transport rate were obtained and discussed using graphs. The velocity declines owing to nanoparticle volume fraction in the stream-wise and cross flow directions in the first result and augment in the second result, while the temperature and concentration upsurge in the first and second results. In addition, the Nusselt number augments due to the Soret number and declines due to the Dufour number in both results, whereas the Sherwood number uplifts due to the Dufour number and shrinks due to the Soret number in both results.
Application of Modified Extended Tanh Technique for Solving Complex Ginzburg-Landau Equation Considering Kerr Law Nonlinearity
(2021) Baleanu, Dumitru; Shallal, Muhannad A.; Mirhosseini-Alizamini, Seyed Mehdi; Rezazadeh, Hadi; Javeed, Shumaila; Baleanu, Dumitru; 56389
The purpose of this work is to find new soliton solutions of the complex Ginzburg-Landau equation (GLE) with Kerr law non-linearity. The considered equation is an imperative nonlinear partial differential equation (PDE) in the field of physics. The applications of complex GLE can be found in optics, plasma and other related fields. The modified extended tanh technique with Riccati equation is applied to solve the Complex GLE. The results are presented under a suitable choice for the values of parameters. Figures are shown using the three and two-dimensional plots to represent the shape of the solution in real, and imaginary parts in order to discuss the similarities and difference between them. The graphical representation of the results depicts the typical behavior of soliton solutions. The obtained soliton solutions are of different forms, such as, hyperbolic and trigonometric functions. The results presented in this paper are novel and reported first time in the literature. Simulation results establish the validity and applicability of the suggested technique for the complex GLE. The suggested method with symbolic computational software such as, Mathematica and Maple, is proven as an effective way to acquire the soliton solutions of nonlinear partial differential equations (PDEs) as well as complex PDEs.
Mathematical design enhancing medical images formulated by a fractal flame operator
(2022) Baleanu, Dumitru; Yahya, Husam; Mohammed, Arkan J.; Al-Saidi, Nadia M. G.; Baleanu, Dumitru; 56389
The interest in using fractal theory and its applications has grown in the field of image processing. Image enhancement is one of the feature processing tools, which aims to improve the details of an image. The enhancement of digital pictures is a challenging task due to the unforeseeable variation in the quality of the captured images. In this study, we present a mathematical model using a local conformable differential operator (LCDO). The proposed model is formulated by the theory of cantor fractal to generalize the definition of LCDO. The main advan-tage of utilizing LCDO for image enhancement is its capability to enhance the low contrast intensities using the coefficient estimate of LCDO. The proposed image enhancement algorithm is tested against different images with different qualities to show that it is robust and can withstand dramatic variations in quality. The quantitative results of Brisque, and Piqe were 30.38 and 35.53 respectively. The comparative consequences indicate that the proposed image enhancement model realizes the best i mage quality assessments. Overall, t his model significantly improves the details of the given datasets, and can potentially help the medical staff during the diagnosis process. A MATLAB programming instru-ment utilized for application and valuation of the image quality measures. A comparison with other image techniques is illustrated regarding the visual review. © 2022, Tech Science Press. All rights reserved.
More Effective Criteria for Oscillation of Second-Order Differential Equations with Neutral Arguments
(2020) Baleanu, Dumitru; Anis, Mona; Baleanu, Dumitru; Muhib, Ali; 56389
The motivation for this paper is to create new criteria for oscillation of solutions of second-order nonlinear neutral differential equations. In more than one respect, our results improve several related ones in the literature. As proof of the effectiveness of the new criteria, we offer more than one practical example.
Numerical study of computer virus reaction diffusion epidemic model
(2021) Baleanu, Dumitru; Baleanu, Dumitru; Ahmed, Nauman; Azam, Shumaila; Raza, Ali; Rafiq, Muhammad; Rehman, Muhammad Aziz-Ur; 56389
Reaction–diffusion systems are mathematical models which link to several physical phenomena. The most common is the change in space and time of the meditation of one or more materials. Reaction–diffusion modeling is a substantial role in the modeling of computer propagation like infectious diseases. We investigated the transmission dynamics of the computer virus in which connected to each other through network globally. The current study devoted to the structure-preserving analysis of the computer propagation model. This manuscript is devoted to finding the numerical investigation of the reaction–diffusion computer virus epidemic model with the help of a reliable technique. The designed technique is finite difference scheme which sustains the important physical behavior of continuous model like the positivity of the dependent variables, the stability of the equilibria. The theoretical analysis of the proposed method like the positivity of the approximation, stability, and consistency is discussed in detail. A numerical example of simulations yields the authentication of the theoretical results of the designed technique.
Numerical solutions of the initial value problem for fractional differential equations by modification of the adomian decomposition method
(De Gruyter Open LTD, 2014) Baleanu, Dumitru; Vaezpour, SM; Baleanu, Dumitru; 56389
In this paper, we extend a reliable modification of the Adomian decomposition method presented in [34] for solving initial value problem for fractional differential equations. In order to confirm the applicability and the advantages of our approach, we consider some illustrative examples.
A Variety of Novel Exact Solutions for Different Models With the Conformable Derivative in Shallow Water
(2020) Baleanu, Dumitru; Kaplan, Melike; Haque, Md. Rabiul; Osman, M. S.; Baleanu, Dumitru; 56389
For different nonlinear time-conformable derivative models, a versatile built-in gadget, namely the generalized exp(-phi(xi))-expansion (GEE) method, is devoted to retrieving different categories of new explicit solutions. These models include the time-fractional approximate long-wave equations, the time-fractional variant-Boussinesq equations, and the time-fractional Wu-Zhang system of equations. The GEE technique is investigated with the help of fractional complex transform and conformable derivative. As a result, we found four types of exact solutions involving hyperbolic function, periodic function, rational functional, and exponential function solutions. The physical significance of the explored solutions depends on the choice of arbitrary parameter values. Finally, we conclude that the GEE method is more effective in establishing the explicit new exact solutions than the exp(-phi(xi))-expansion method.
A New Dynamic Scheme via Fractional Operators on Time Scale
(2020) Baleanu, Dumitru; 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.