Fen - Edebiyat Fakültesi
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Browsing Fen - Edebiyat Fakültesi by Journal "Abstract and Applied Analysis"
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Article A generalized q-mittag-leffler function by q-captuo fractional linear equations(Hindawi Publishing Corporation, 2012) Abdeljawad, Thabet; Baleanu, Dumitru; Baleanu, DumitruSome Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler functions. The method of successive approximation is used to obtain the solutions. The obtained q-version of Mittag-Leffler function is thought as the q-analogue of the one introduced previously by Kilbas and SaigoArticle A Jacobi Collocation Method for Solving Nonlinear Burgers-Type Equations(Hindawi LTD, 2013) Baleanu, Dumitru; Baleanu, Dumitru; Bhrawy, A. H.; Abdelkawy, M. A.; 56389We solve three versions of nonlinear time-dependent Burgers-type equations. The Jacobi-Gauss-Lobatto points are used as collocation nodes for spatial derivatives. This approach has the advantage of obtaining the solution in terms of the Jacobi parameters alpha and beta In addition, the problem is reduced to the solution of the system of ordinary differential equations (SODEs) in time. This system may be solved by any standard numerical techniques. Numerical solutions obtained by this method when compared with the exact solutions reveal that the obtained solutions produce high-accurate results. Numerical results show that the proposed method is of high accuracy and is efficient to solve the Burgers-type equation. Also the results demonstrate that the proposed method is a powerful algorithm to solve the nonlinear partial differential equations.Article A k-Dimensional System of Fractional Finite Difference Equations(Hindawi LTD, 2013) Baleanu, Dumitru; Doha, E. H.; Bhrawy, A. H.; Abdelkawy, M. A.; 56389We solve three versions of nonlinear time-dependent Burgers-type equations. The Jacobi-Gauss-Lobatto points are used as collocation nodes for spatial derivatives. This approach has the advantage of obtaining the solution in terms of the Jacobi parameters alpha and beta In addition, the problem is reduced to the solution of the system of ordinary differential equations (SODEs) in time. This system may be solved by any standard numerical techniques. Numerical solutions obtained by this method when compared with the exact solutions reveal that the obtained solutions produce high-accurate results. Numerical results show that the proposed method is of high accuracy and is efficient to solve the Burgers-type equation. Also the results demonstrate that the proposed method is a powerful algorithm to solve the nonlinear partial differential equations.Article A k-Dimensional System of Fractional Finite Difference Equations(2014) Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; 56389We investigate the existence of solutions for a k-dimensional system of fractional finite difference equations by using the Kranoselskii's fixed point theorem. We present an example in order to illustrate our results.Article A k-Dimensional System of Fractional Neutral Functional Differential Equations with Bounded Delay(Hindawi LTD, 2014) Baleanu, Dumitru; Nazemi, Sayyedeh Zahra; Rezapour, Shahram; 56389In 2010, Agarwal et al. studied the existence of a one-dimensional fractional neutral functional differential equation. In this paper, we study an initial value problem for a class of k-dimensional systems of fractional neutral functional differential equations by using Krasnoselskii's fixed point theorem. In fact, our main result generalizes their main result in a sense..Article A Local Fractional Variational Iteration Method for Laplace Equation Within Local Fractional Operators(Hindawi LTD, 2013) Baleanu, Dumitru; Baleanu, Dumitru; Yang, Xiao-Jun; 56389he local fractional variational iteration method for local fractional Laplace equation is investigated in this paper. The operators are described in the sense of local fractional operators. The obtained results reveal that the method is very effective.Article A Modified Generalized Laguerre-Gauss Collocation Method for Fractional Neutral Functional-Differential Equations on the Half-Line(Hindawi LTD, 2014) Baleanu, Dumitru; Alzahrani, Abdulrahim A.; Baleanu, Dumitru; Alhamed, Yahia A.; 56389The modified generalized Laguerre-Gauss collocation (MGLC) method is applied to obtain an approximate solution of fractional neutral functional-differential equations with proportional delays on the half-line. The proposed technique is based on modified generalized Laguerre polynomials and Gauss quadrature integration of such polynomials. The main advantage of the present method is to reduce the solution of fractional neutral functional-differential equations into a system of algebraic equations. Reasonable numerical results are achieved by choosing few modified generalized Laguerre-Gauss collocation points. Numerical results demonstrate the accuracy, efficiency, and versatility of the proposed method on the half-line.Article A New Class of Contraction in B -Metric Spaces and Applications(Hindawi Limited, 2017) Taş, Kenan; Kaushik, P.; Kumar, S.; 4971A novel class of α-β-contraction for a pair of mappings is introduced in the setting of b-metric spaces. Existence and uniqueness of coincidence and common fixed points for such kind of mappings are investigated. Results are supported with relevant examples. At the end, results are applied to find the solution of an integral equation.Article A New Class of Contraction in b -Metric Spaces and Applications(2017) Kaushik, P.; Kumar, S.; Kenan, Taş; 4971A novel class of α-β-contraction for a pair of mappings is introduced in the setting of b-metric spaces. Existence and uniqueness of coincidence and common fixed points for such kind of mappings are investigated. Results are supported with relevant examples. At the end, results are applied to find the solution of an integral equation. © 2017 Preeti Kaushik et al.Article A New Impulsive Multi-Orders Fractional Differential Equation Involving Multipoint Fractional Integral Boundary Conditions(Hindawi LTD, 2014) Baleanu, Dumitru; Liu, Sanyang; Zhang, Lihong; Baleanu, Dumitru; 56389A new impulsive multi-orders fractional differential equation is studied. The existence and uniqueness results are obtained for a nonlinear problem with fractional integral boundary conditions by applying standard fixed point theorems. An example for the illustration of the main result is presented.Article A New Impulsive Multi-Orders Fractional Differential Equation Involving Multipoint Fractional Integral Boundary Conditions(Hindawi LTD, 2014) Baleanu, Dumitru; Liu, Sanyang; Baleanu, Dumitru; 56389A new impulsive multi-orders fractional differential equation is studied. The existence and uniqueness results are obtained for a nonlinear problem with fractional integral boundary conditions by applying standard fixed point theorems. An example for the illustration of the main result is presented.Article A Pseudospectral Algorithm for Solving Multipantograph Delay Systems on a Semi-Infinite Interval Using Legendre Rational Functions(Hindawi LTD, 2014) Baleanu, Dumitru; Baleanu, Dumitru; Bhrawy, A. H.; Hafez, R. M.; 56389A new Legendre rational pseudospectral scheme is proposed and developed for solving numerically systems of linear and nonlinear multipantograph equations on a semi-infinite interval. A Legendre rational collocation method based on Legendre rational- Gauss quadrature points is utilized to reduce the solution of such systems to systems of linear and nonlinear algebraic equations. In addition, accurate approximations are achieved by selecting few Legendre rational- Gauss collocation points. The numerical results obtained by this method have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively limited nodes used, the absolute error in our numerical solutions is sufficiently small.Article A unique common triple fixed point theorem for hybrid pair of maps(Hindawi Publishing Corporation, 2012) Taş, Kenan; Kishore, G. N. V.; Taş, Kenan; 4971We obtain a unique common triple fixed point theorem for hybrid pair of mappings in metric spaces. Our result extends the recent results of B. Samet and C. Vetro (2011). We also introduced a suitable example supporting our resultEditorial Advanced Theoretical and Applied Studies of Fractional Differential Equations(Hindawi Publishing Corporation, 2013) Baleanu, Dumitru; Trujillo, Juan J.; Ahmad, Bashir; 56389Article Advances On Integrodifferential Equations and Transforms(Hindawi Publishing Corporation, 2015) Baleanu, Dumitru; Yang, Xiao-Jun; Baleanu, Dumitru; Nieto, Juan J.; Hristov, Jordan,; 56389Article Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems In Hilbert Spaces(Hindawi LTD, 2013) Baleanu, Dumitru; Debbouche, Amar; Baleanu, Dumitru; 56389We study a class of fractional stochastic dynamic control systems of Sobolev type in Hilbert spaces. We use fixed point technique, fractional calculus, stochastic analysis, and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions for approximate controllability is formulated and proved. An example is also given to provide the obtained theory.Article Asymptotically linear solutions for some linear fractional differential equations(Hindawi Publishing Corporation, 2010) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.We establish here that under some simple restrictions on the functional coefficient a(t) the fractional differential equation 0D(t)(alpha)[tx' - x + x(0)] + a(t)x = 0, t > 0, has a solution expressible as ct + d + o(1) for t -> +infinity, where D-0(t)alpha designates the Riemann-Liouville derivative of order alpha is an element of (0, 1) and c, d is an element of RArticle Behavior of the Solutions for Predator-Prey Dynamic Systems With Beddington-Deangelis Type Functional Response On Periodic Time Scales İn Shifts(Hindawi Limited, 2016) Kaymakçalan, Billur; Güvenilir, Ayşe Feza; Kaymakçalan, Billur; 109448We consider two-dimensional predator-prey system with Beddington-DeAngelis type functional response on periodic time scales in shifts. For this special case we try to find under which conditions the system has δ ± -periodic solution. © 2016 Neslihan Nesliye Pelen et al.Article Certain Inequalities Involving the Fractional q-Integral Operators(Hindawi LTD, 2014) Baleanu, Dumitru; Agarwal, Ravi P.; 56389We establish some inequalities involving Saigo fractional q-integral operator in the theory of quantum calculus by using the two parameters of deformation, q(1) and q(2), whose special cases are shown to yield corresponding inequalities associated with Riemann-Liouville and Kober fractional q-integral operators, respectively. Furthermore, we also consider their relevance with other related known results.Article Chebyshev Type Integral Inequalities Involving the Fractional Hypergeometric Operators(Hindawi LTD, 2014) Baleanu, Dumitru; Purohit, S. D.; 56389By making use of the fractional hypergeometric operators, we establish certain new fractional integral inequalities for synchronous functions which are related to the weighted version of the Chebyshev functional. Some consequent results and special cases of the main results are also pointed out.
