Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 14Citation - Scopus: 18Existence Theory and Numerical Simulation of HIV-I Cure Model with New Fractional Derivative Possessing a Non-Singular Kernel(Springeropen, 2019) Aliyu, Aliyu Lsa; Alshomrani, Ali Saleh; Li, Yongjin; Inc, Mustafa; Baleanu, DumitruIn this research work, a mathematical model related to HIV-I cure infection therapy consisting of three populations is investigated from the fractional calculus viewpoint. Fractional version of the model under consideration has been proposed. The proposed model is examined by using the Atangana-Baleanu fractional operator in the Caputo sense (ABC). The theory of Picard-Lindelof has been employed to prove existence and uniqueness of the special solutions of the proposed fractional-order model. Further, it is also shown that the non-negative hyper-plane a positively invariant region for the underlying model. Finally, to analyze the results, some numerical simulations are carried out via a numerical technique recently devised for finding approximate solutions of fractional-order dynamical systems. Upon comparison of the numerical simulations, it has been demonstrated that the proposed fractional-order model is more accurate than its classical version. All the necessary computations have been performed using MATLAB R2018a with double precision arithmetic.Erratum Citation - WoS: 5Citation - Scopus: 1Retracted: Retracted: Fuzzy Fractional Ostrowski Inequality With Caputo Differentiability (Retracted Article. See 2013)(Springeropen, 2013) Allahviranloo, Tofigh; Avazpour, Lutfi; Ebadi, Mohammad J.; Baleanu, Dumitru; Salahshour, SoheilThe use of fractional inequalities in mathematical models is increasingly widespread in recent years. In this manuscript, we firstly propose the right Caputo derivative of fuzzy-valued functions about fractional order v (0 < v < 1). To this end, we consider two types of differentiability (similar to the non-fractional case). Then we derive the equivalent integral forms of original fuzzy fractional differential equations. Finally, we prove the fuzzy Ostrowski inequality involving three functions under Caputo's differentiability. In this regard, we state some new results.Article Citation - WoS: 2Citation - Scopus: 1Coupled 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, ManishWe 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: 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: 8Citation - Scopus: 15Computation 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, SajjadIn 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.Article Citation - WoS: 152Citation - Scopus: 60A Semigroup-Like Property for Discrete Mittag-Leffler Functions(Springeropen, 2012) Abdeljawad, Thabet; Jarad, Fahd; Baleanu, DumitruDiscrete Mittag-Leffler function of order 0 < alpha a parts per thousand currency sign 1, , lambda not equal 1, satisfies the nabla Caputo fractional linear difference equation (C)del(alpha)(0)(t) = lambda x(t), x(0) = 1, t is an element of N-1 = {1, 2, 3, ...}. Computations can show that the semigroup identity E alpha(lambda, z1)E alpha(lambda, z2) = E alpha(lambda, z1 + z2) does not hold unless lambda = 0 or alpha = 1. In this article we develop a semigroup property for the discrete Mittag-Leffler function in the case alpha a dagger 1 is just the above identity. The obtained semigroup identity will be useful to develop an operator theory for the discrete fractional Cauchy problem with order alpha a (0, 1).