Matematik Bölümü Yayın Koleksiyonu

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

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  • Article
    Citation - WoS: 2
    Citation - Scopus: 1
    Coupled Common Fixed Point Results Involving (φ,ψ)-Contractions in Ordered Generalized Metric Spaces With Application To Integral Equations
    (Springeropen, 2013) Tas, Kenan; Gupta, Neetu; Jain, Manish
    We establish some coupled coincidence and coupled common fixed point theorems for the mixed g-monotone mappings satisfying -contractive conditions in the setting of ordered generalized metric spaces. Presented theorems extend and generalize the very recent results of Choudhury and Maity (Math. Comput. Model. 54(1-2):73-79, 2011). To illustrate our results, an example and an application to integral equations have also been given. MSC: 54H10, 54H25.
  • Article
    Citation - WoS: 67
    Citation - Scopus: 75
    The 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, Dumitru
    We 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, Dumitru
    This 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: 22
    Citation - Scopus: 25
    Attractivity 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, Dumitru
    In 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: 24
    Citation - Scopus: 19
    Refinement 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: 7
    Citation - Scopus: 8
    Determination 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-h
    In 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: 10
    Citation - Scopus: 16
    Reconstructing 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 Hoang
    In 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: 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.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 16
    The 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: 8
    Citation - Scopus: 15
    Computation of Iterative Solutions Along With Stability Analysis To a Coupled System of Fractional Order Differential Equations
    (Springeropen, 2019) Abdeljawad, Thabet; Shah, Kamal; Jarad, Fahd; Arif, Muhammad; Ali, Sajjad
    In this research article, we investigate sufficient results for the existence, uniqueness and stability analysis of iterative solutions to a coupled system of the nonlinear fractional differential equations (FDEs) with highier order boundary conditions. The foundation of these sufficient techniques is a combination of the scheme of lower and upper solutions together with the method of monotone iterative technique. With the help of the proposed procedure, the convergence criteria for extremal solutions are smoothly achieved. Furthermore, a major aspect is devoted to the investigation of Ulam-Hyers type stability analysis which is also established. For the verification of our work, we provide some suitable examples along with their graphical represntation and errors estimates.