Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 67Citation - Scopus: 75The Extended Fractional Caputo-Fabrizio Derivative of Order 0 ≤ Σ < 1 on Cr[0,1] and the Existence of Solutions for Two Higher-Order Series-Type Differential Equations(Springeropen, 2018) Mousalou, Asef; Rezapour, Shahram; Baleanu, DumitruWe extend the fractional Caputo-Fabrizio derivative of order 0 <= sigma < 1 on C-R[0,1] and investigate two higher-order series-type fractional differential equations involving the extended derivation. Also, we provide an example to illustrate one of the main results.Article On a new class of fractional operators(Springeropen, 2017) Jarad, Fahd; Uğurlu, Ekin; Abdeljawad, Thabet; Baleanu, DumitruThis manuscript is based on the standard fractional calculus iteration procedure on conformable derivatives. We introduce new fractional integration and differentiation operators. We define spaces and present some theorems related to these operators.Article Citation - WoS: 22Citation - Scopus: 25Attractivity for a K-Dimensional System of Fractional Functional Differential Equations and Global Attractivity for a K-Dimensional System of Nonlinear Fractional Differential Equations(Springeropen, 2014) Nazemi, Sayyedeh Zahra; Rezapour, Shahram; Baleanu, DumitruIn this paper, we present some results for the attractivity of solutions for a k-dimensional system of fractional functional differential equations involving the Caputo fractional derivative by using the classical Schauder's fixed-point theorem. Also, the global attractivity of solutions for a k-dimensional system of fractional differential equations involving Riemann-Liouville fractional derivative are obtained by using Krasnoselskii's fixed-point theorem. We give two examples to illustrate our main results.Article Citation - WoS: 24Citation - Scopus: 19Refinement Multidimensional Dynamic Inequalities With General Kernels and Measures(Springeropen, 2019) Rezk, Haytham M.; Abohela, Islam; Baleanu, Dumitru; Saker, Samir H.Using the properties of superquadratic and subquadratic functions, we establish some new refinement multidimensional dynamic inequalities of Hardy's type on time scales. Our results contain some of the recent results related to classical multidimensional Hardy's and Polya-Knopp's inequalities on time scales. To show motivation of the paper, we apply our results to obtain some particular multidimensional cases and provide refinements of some Hardy-type inequalities known in the literature.Article Citation - WoS: 7Citation - Scopus: 8Determination of Source Term for the Fractional Rayleigh-Stokes Equation With Random Data(Springeropen, 2019) Baleanu, Dumitru; Nguyen Hoang Luc; Nguyen-H Can; Tran Thanh Binh; Binh, Tran Thanh; Luc, Nguyen Hoang; Can, Nguyen-hIn this article, we consider the problem of finding a source term of a Rayleigh-Stokes equation. Our problem is not well-posed in the sense of Hadamard. The sought solution does not depend continuously on the given data. Using the truncation method and some new techniques on trigonometric estimators, we give the regularized solution. Moreover, the mean square error and convergence rates are established.Article Citation - WoS: 10Citation - Scopus: 16Reconstructing the Right-Hand Side of a Fractional Subdiffusion Equation From the Final Data(Springeropen, 2020) Baleanu, Dumitru; Long, Le Dinh; Can, Nguyen-Huu; Luc, Nguyen HoangIn this study, we study an inverse source problem for the time-fractional diffusion equation, where the final data t=Tare given. We show that our problem is ill-posed in the sense of Hadamard. Applying a truncation method, we give the regularized solution. Finally, convergence estimates under a priori and a posteriori parameter choice rules are proved.Article Citation - WoS: 6Citation - Scopus: 7Fractional Spectral Differentiation Matrices Based on Legendre Approximation(Springeropen, 2020) Baleanu, Dumitru; Ghorbani, AsgharA 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.Article Citation - WoS: 14Citation - Scopus: 16The Invariant Subspace Method for Solving Nonlinear Fractional Partial Differential Equations With Generalized Fractional Derivatives(Springeropen, 2020) Kader, Abass H. Abdel; Baleanu, Dumitru; Latif, Mohamed S. Abdel; Abdel Latif, Mohamed S.; Abdel Kader, Abass H.In this paper, we show that the invariant subspace method can be successfully utilized to get exact solutions for nonlinear fractional partial differential equations with generalized fractional derivatives. Using the invariant subspace method, some exact solutions have been obtained for the time fractional Hunter-Saxton equation, a time fractional nonlinear diffusion equation, a time fractional thin-film equation, the fractional Whitman-Broer-Kaup-type equation, and a system of time fractional diffusion equations.Article Citation - WoS: 16Citation - Scopus: 14Approximate Controllability of a Semilinear Impulsive Stochastic System With Nonlocal Conditions and Poisson Jumps(Springeropen, 2020) Ravikumar, K.; Baleanu, Dumitru; Anguraj, A.The objective of this paper is to investigate the approximate controllability of a semilinear impulsive stochastic system with nonlocal conditions and Poisson jumps in a Hilbert space. Nonlocal initial condition is a generalization of the classical initial condition and is motivated by physical phenomena. The results are obtained by using Sadovskii's fixed point theorem. Finally, an example is provided to illustrate the effectiveness of the obtained result.Article Citation - WoS: 134Citation - Scopus: 143Analyzing Transient Response of the Parallel Rcl Circuit by Using the Caputo-Fabrizio Fractional Derivative(Springeropen, 2020) Baleanu, Dumitru; Rezapour, Shahram; Alizadeh, ShahramIn this paper, the transient response of the parallel RCL circuit with Caputo-Fabrizio derivative is solved by Laplace transforms. Also, the graphs of the obtained solutions for the different orders of the fractional derivatives are compared with each other and with the usual solutions. Finally, they are compared with practical and laboratory results.