Matematik Bölümü

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Citation - WoS: 6
Citation - Scopus: 6
A caputo fractional order boundary value problem with integral boundary conditions
(Eudoxus Press, Llc, 2013) Babakhani, Azizollah; Abdeljawad, Thabet; Abdeljawad, Thabet; Matematik
In this paper, we discuss existence and uniqueness of solutions to nonlinear fractional order ordinary differential equations with integral boundary conditions in an ordered Banach space. We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function. The nonlinear alternative of the Leray- Schauder type Theorem is the main tool used here to establish the existence and the Banach contraction principle to show the uniqueness of the solution under certain conditions. The compactness of solutions set is also investigated and an example is included to show the applicability of our results.
Citation - WoS: 24
A chebyshev-laguerre-gauss-radau collocation scheme for solving a time fractional sub-diffusion equation on a semi-infinite domain
(Editura Acad Romane, 2015) Bhrawy, A. H.; Baleanu, Dumitru; Abdelkawy, M. A.; Alzahrani, A. A.; Baleanu, D.; Alzahrani, E. O.; Matematik
We propose a new efficient spectral collocation method for solving a time fractional sub-diffusion equation on a semi-infinite domain. The shifted Chebyshev-Gauss-Radau interpolation method is adapted for time discretization along with the Laguerre-Gauss-Radau collocation scheme that is used for space discretization on a semi-infinite domain. The main advantage of the proposed approach is that a spectral method is implemented for both time and space discretizations, which allows us to present a new efficient algorithm for solving time fractional sub-diffusion equations.
Citation - WoS: 11
Citation - Scopus: 13
A Composition Formula of the Pathway Integral Transform Operator
(Aracne Editrice, 2014) Baleanu, Dumitru; Baleanu, Dumitru; Agarwal, Praveen; 56389; Matematik
In the present paper, we aim at presenting composition formula of integral transform operator due to Nair, which is expressed in terms of the generalized Wright hypergeometric function, by inserting the generalized Bessel function of the first kind w(v) z). Furthermore the special cases for the product of trigonometric functions are also consider.
Citation - Scopus: 7
A Dynamical and Sensitivity Analysis of the Caputo Fractional-Order Ebola Virus Model: Implications for Control Measures
(Thammasat University, 2023) Ahmed, I.; Jarad, Fahd; Yusuf, A.; Tariboon, J.; Muhammad, M.; Jarad, F.; Mikailu, B.B.; 234808; Matematik
The recurrence of outbreaks in cases of Ebola virus among African countries remains one of the greatest issues of concern. Practices such as hunting or consumption of contam-inated bush meat, unsafe funeral practices, and environmental contamination have all been implicated as possible contributors. This paper investigates the transmission dynamics of the Ebola virus model in the setting of a Caputo fractional-order derivative that accounts for both direct and indirect transmissions of the virus. By employing the concept of fixed theorems, we derived the existence and uniqueness results of the model. Moreover, we analyzed the forward normalized sensitivity indices to identify the critical parameters for controlling the infection and found that reducing the contact rate between infected individuals and susceptible vectors is vital to limiting the virus’s spread. Comparing the proposed fractional-order model with those of the previously developed integer-order model numerically, we found that the proposed model provides more reliable information on the model’s dynamics. Thus, we conclude that the Caputo fractional-order operator is a precise tool for describing the proposed model behavior and can help understand the complexities of Ebola virus disease outbreaks. © 2023, Thammasat University. All rights reserved.
Citation - WoS: 4
Citation - Scopus: 6
A fractional derivative inclusion problem via an integral boundary condition
(Eudoxus Press, Llc, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Moghaddam, Mehdi; Mohammadi, Hakimeh; Rezapour, Shahram; Matematik
We investigate the existence of solutions for the fractional differential inclusion (c)D(alpha)x(t) is an element of F(t, x(t)) (equipped with the boundary value problems x(0) = 0 and x(1) = integral(eta)(0) x(s)ds, where 0 < eta < 1, 1 < alpha <= 2, D-c(alpha) is the standard Caputo differentiation and F : [0, 1] x R -> 2(R) is a compact valued multifunction. An illustrative example is also discussed.
Citation - WoS: 5
A fractional finite difference inclusion
(Eudoxus Press, Llc, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; Matematik
In this manuscript we investigated the fractional finite difference inclusion Delta(mu)(mu-2) x(t) is an element of F(t, x(t), Delta x(t)) via the boundary conditions Delta x(b + mu) = A and x(mu - 2) = B, where 1 <= 2, A,B is an element of R and F :N-mu-2(b+mu+2) x R -> 2(R) is a compact valued multifunction.
Citation - Scopus: 5
A Frational Finite Differene Inclusion
(Eudoxus Press, LLC, 2016) Baleanu, D.; Abdeljawad, Thabet; Rezapour, S.; Salehi, S.; Matematik
In this manuscript, we investigated the fractional finite difference inclusion (formula presented) via the boundary conditions Δx(b+μ)=A and x(μ-2)=B, where 1 < μ ≤ 2, A, B ε ℝ. and (formula presented) is a compact valued multifunction. © 2016 by Eudoxus Press, LLC, All rights reserved.
Citation - WoS: 1
Citation - Scopus: 2
A Homotopy Perturbation Solution for Solving Highly Nonlinear Fluid Flow Problem Arising in Mechanical Engineering
(Amer inst Physics, 2018) Khan, Yasir; Baleanu, Dumitru; Akgul, Ali; Faraz, Naeem; Inc, Mustafa; Akgul, Esra Karatas; Baleanu, Dumitru; 56389; Matematik
In this paper, a highly nonlinear equations are treated analytically via homotopy perturbation method for fluid mechanics problem. The non-linear differential equations are transformed to a coupled non-linear ordinary, differential equations via similarity transformations. Graphical results are presented and discussed for various physical parameters.
Citation - Scopus: 17
A Jacobi Collocation Method for Troesch'S Problem in Plasma Physics
(Editura Academiei Romane, 2014) Doha, E.H.; Baleanu, Dumitru; Baleanu, D.; Bhrawi, A.H.; Hafez, R.M.; 56389; Matematik
In this paper, we propose a numerical approach for solving Troesch's problem which arises in the confinement of a plasma column by radiation pressure. It is also an inherently unstable two-point boundary value problem. The spatial approximation is based on shifted Jacobi-Gauss collocation method in which the shifted Jacobi-Gauss points are used as collocation nodes. The results presented here demonstrate reliability and efficiency of the method.
Citation - Scopus: 1
A Lebesgue İntegrable Space of Boehmians for A Class of Dk Transformations
(Eudoxus Press, LLC, 2018) Al-Omari, S.; Baleanu, Dumitru; Baleanu, D.; 56389; Matematik
Boehmians are objects obtained by an abstract algebraic construction similar to that of field of quotients and it in some cases just gives the field of quotients. As Boehmian spaces are represented by convolution quotients, integral transforms have a natural extension onto appropriately defined spaces of Boehmians. In this paper, we have defined convolution products and a class of delta sequences and have examined the axioms necessary for generating the Dk spaces of Boehmians. The extended Dk transformation has therefore been defined as a one-to-one onto mapping continuous with respect to Δ and δ convergences. Over and above, it has been asserted that the necessary and sufficient conditions for an integrable sequence to be in the range of the Dk transformation is that the class of quotients belongs to the range of the representative. Further results related to the inverse problem are also discussed. © 2018 EUDOXUS PRESS, LLC.
Citation - WoS: 8
Citation - Scopus: 8
A new method for dissipative dynamic operator with transmission conditions
(Springer Basel Ag, 2018) Uğurlu, Ekin; Ugurlu, Ekin; Tas, Kenan; Taş, Kenan; 238990; 4971; Matematik
In this paper, we investigate the spectral properties of a boundary value transmission problem generated by a dynamic equation on the union of two time scales. For such an analysis we assign a suitable dynamic operator which is in limit-circle case at infinity. We also show that this operator is a simple maximal dissipative operator. Constructing the inverse operator we obtain some information about the spectrum of the dissipative operator. Moreover, using the Cayley transform of the dissipative operator we pass to the contractive operator which is of the class With the aid of the minimal function we obtain more information on the dissipative operator. Finally, we investigate other properties of the contraction such that multiplicity of the contraction, unitary colligation with basic operator and CMV matrix representation associated with the contraction.
Citation - WoS: 5
Citation - Scopus: 6
A note on fractional neutral integro-differential inclusions with state-dependent delay in Banach spaces
(Eudoxus Press, Llc, 2016) Suganya, Selvaraj; Baleanu, Dumitru; Baleanu, Dumitru; Arjunan, Mani Mallika; Matematik
We have applied different fixed point theorems to examine the existence results for fractional neutral integro-differential inclusions (FNIDI) with state-dependent delay (SDD) in Banach spaces. We tend to conjointly discuss the cases once the multivalued nonlinear term takes convex values further as nonconvex values. An example is offered to demonstrate the obtained results.
Citation - Scopus: 3
A Note On Sobolev Form Fractional Integro-Differential Equation With State-Dependent Delay Via Resolvent Operators
(Cambridge Scientific Publishers, 2017) Mallika, D.; Baleanu, Dumitru; Suganya, S.; Baleanu, D.; Arjunan, M.M.; 56389; Matematik
This paper explores the new existence and uniqueness of mild solutions for a class of Sobolev form fractional integro-differential equation (in short SFFIDE) with state-dependent delay (in short SDD) and nonlocal conditions (in short NLCs) via resolvent operators in Banach spaces. By making use of Banach contraction principle and Krasnoselskii fixed point theorem (in short FPT) along with resolvent operators and fractional calculus, we develop the sought outcomes. An illustration is furthermore provided to demonstrate the acquired concepts. © CSP - Cambridge, UK; I & S - Florida, USA, 2017.
Citation - WoS: 9
Citation - Scopus: 10
A Perturbative Analysis Of Nonlinear Cubic-Quintic Duffing Oscillators
(Editura Acad Romane, 2014) Sayevand, Khosro; Baleanu, Dumitru; Baleanu, Dumitru; Fardi, Mojtaba; 56389; Matematik
Duffing oscillators comprise one of the canonical examples of Hamilton systems. The presence of a quintic term makes the cubic-quintic Duffing oscillator more complex and interesting to study. In this paper, the homotopy analysis method (HAM) is used to obtain the analytical solution for the nonlinear cubic-quintic Duffing oscillators. The HAM helps to obtain the frequency omega in the form of approximation series of a convergence control parameter (h) over bar. The valid region of (h) over bar is determined by plotting the omega - (h) over bar curve and afterwards we compared the obtained results with the exact solutions.
Citation - WoS: 4
Citation - Scopus: 4
A Reduced-Order Finite Difference Scheme Based on POD for Fractional Stochastic Advection-Diffusion Equation
(Springer int Publ Ag, 2023) Soori, Z.; Aminataei, A.; Baleanu, D.; 56389
his article introduces a new scheme for the fractional stochastic advection-diffusion equation (FSA-DE) in time where the fractional term is expressed in Caputo sence of order (0
Citation - Scopus: 2
A Study of A Multi-Degree of Freedom Fractional Order Damped Oscillatory System
(Politechnica University of Bucharest, 2018) Agila, A.; Baleanu, Dumitru; Baleanu, D.; 56389; Matematik
The fractional calculus is a promising applied mathematical tool to different disciplines. Some dynamic systems can be precisely represented as fractional systems due to their physical properties. A multi-degree of freedom fractional damped oscillatory system is mathematically modeled by means of fractional order differential equation. In this model the damping force acting on the vibrating system is proportional to the fractional derivative of the displacement. The variable-order Caputo fractional derivative and an approximation technique are utilized to obtain the system responses. The approximation is accomplished by using a numerical discretization technique. Based on the definition of variable-order Caputo fractional derivative, the system response is investigated for different system parameters. The approximation of the system response is verified to show the efficiency of the applied techniques. © 2018 Politechnica University of Bucharest. All rights reserved.
Citation - Scopus: 6
A Survey on Interpolative and Hybrid Contractions
(Springer, 2021) Karapınar, E.; Karapınar, Erdal; 19184; Matematik
In this chapter, we consider the distinct hybrid type contractions in various abstract spaces. In this work, hybrid contraction refers to combination of not only linear and nonlinear contractions, but also interpolative contractions. The main goal of the chapter is to clarify the metric fixed point theory literature by using the hybrid type contractions that unify several well-known results. © 2021, Springer Nature Switzerland AG.
Citation - WoS: 0
Citation - Scopus: 1
Adapting Integral Transforms to Create Solitary Solutions for Partial Differential Equations Via A New Approach
(New York Business Global Llc, 2023) Saadeh, Rania; Baleanu, Dumitru; Qazza, Ahmad; Burqan, Aliaa; Baleanu, Dumitru; 56389; Matematik
In this article, a new effective technique is implemented to solve families of nonlinear partial differential equations (NLPDEs). The proposed method combines the double ARA-Sumudu transform with the numerical iterative method to get the exact solutions of NLPDEs. The suc-cessive iterative method was used to find the solution of nonlinear terms of these equations. In order to show the efficiency and applicability of the presented method, some physical applications are analyzed and illustrated, and to defend our results, some numerical examples and figures are discussed.
Citation - Scopus: 1
Advanced Mathematical and Statistical Tools in the Dynamic Modeling and Simulation of Gene-Environment Regulatory Networks
(Springer New York LLC, 2014) Defterli, Ö.; Defterli, Özlem; Purutçuoğlu, V.; Weber, G.-W.; 31401; Matematik
Citation - Scopus: 5
Advanced Topics in Fractional Differential Equations A Fixed Point Approach
(Springer Nature, 2023) Benchohra, M.; Karapınar, Erdal; Karapınar, E.; Lazreg, J.E.; Salim, A.; 19184; Matematik

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