WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 5Citation - Scopus: 7On Some Self-Adjoint Fractional Finite Difference Equations(Eudoxus Press, Llc, 2015) Baleanu, Dumitru; Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; MatematikRecently, the existence of solution for the fractional self-adjoint equation Delta(nu)(nu-1) (p Delta y)(t) = h(t) for order 0 < nu <= 1 was reported in [9]. In this paper, we investigated the self-adjoint fractional finite difference equation Delta(nu)(nu-2)(p Delta u(t) = j(t,p(t+nu - 2)) via the boundary conditions y(nu - 2) = 0 , such that Delta y(nu - 2) = 0 and Delta y(nu+b) = 0. Also, we analyzed the self-adjoing fractional finite difference equation Delta(nu()(nu-2)p Delta(2)y)(t) = j(t,[(t+nu - 2)Delta(2)y(t+nu-3)) via the boundary conditions y(nu - 2) = 0, Delta y(nu - 2) = 0, Delta(2)y(nu - 2) = 0 and Delta 2y(nu+b) = 0. Finally, we conclude a result about the existence of solution for the general equation Delta(nu()(nu-2)p Delta(m)y)(t) = h(t,p(t+nu - m - 1)Delta(m)y(t+nu - m - 1)) via the boundary conditions y(nu - 2) = Delta y(nu - 2) = Delta(2)y(nu - 2) = center dot center dot center dot Delta(m)y(nu+b) = 0 for oder 1 < nu <= 2.Article Citation - WoS: 4Citation - Scopus: 6A Fractional Derivative Inclusion Problem Via an Integral Boundary Condition(Eudoxus Press, Llc, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Moghaddam, Mehdi; Mohammadi, Hakimeh; Rezapour, Shahram; MatematikWe 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.Article Citation - WoS: 5Citation - Scopus: 6A 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; MatematikWe 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.Article Citation - WoS: 35Some Theorems and Examples of Cone Banach Spaces(Eudoxus Press, Llc, 2010) Abdeljawad, Thabet; Abdeljawad, Thabet; Turkoglu, Duran; Abuloha, Muhib; MatematikIn this paper, by defining a cone norm parallel to.parallel to(A) on E over itself which behaves like the absolute value norm on R, we construct examples of cone Banach spaces. Namely, we define the m-Euclidian cone normed space E-m, E-infinity and the space C-E(S) of continuous functions in cones, to generalize the Banach spaces R-m, l(infinity) and C [a, b], respectively. Some basic lemmas and theorems are also proved to help in the construction and in the proof of completeness of the above mentioned examples of cone normed spaces.Article Citation - WoS: 6Citation - Scopus: 6A Caputo Fractional Order Boundary Value Problem With Integral Boundary Conditions(Eudoxus Press, Llc, 2013) Babakhani, Azizollah; Abdeljawad, Thabet; Abdeljawad, Thabet; MatematikIn 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.Article Citation - WoS: 11Citation - Scopus: 12On the Generalized Stieltjes Transform of Fox's Kernel Function and Its Properties in the Space of Generalized Functions(Eudoxus Press, Llc, 2017) Al-Omari, Shrideh Khalaf Qasem; Baleanu, Dumitru; Baleanu, Dumitru; MatematikIn this paper, a Stieltjes transform enfolding some Fox's H-function has been investigated on certain class of generalized functions named as Boehmians. By developing two spaces of Boehmians, the extended transform has been inspected and some general properties are also obtained. An inverse problem is also discussed in some detail.Article Citation - WoS: 3Citation - Scopus: 4A Gregus Type Common Fixed Point Theorem of Set-Valued Mappings in Cone Metric Spaces(Eudoxus Press, Llc, 2011) Abdeljawad, Thabet; Abdeljawad, T.; Murthy, P. P.; Taş, Kenan; Tas, K.; MatematikThe main purpose of this paper is to obtain a common fixed point theorem for a pair of set-valued mappings of Gregus type condition in cone metric spaces, so that the main result obtained in [13] will be generalized to cone metric spaces. The cone under consideration will be normal with normal constant K = 1.Article Citation - WoS: 7Citation - Scopus: 7Coupled Fixed Point Theorems for Generalized Symmetric Contractions in Partially Ordered Metric Spaces and Applications(Eudoxus Press, Llc, 2014) Jain, M.; Taş, Kenan; Tas, K.; Rhoades, B. E.; Gupta, N.; MatematikIn the setting of partially ordered metric spaces, we introduce the notion of generalized symmetric g-Meir-Keeler type contractions and use the notion to establish the existence and uniqueness of coupled common fixed points. Our notion extends the notion of generalized symmetric Meir-Keeler contractions given by Berinde et. al. [V. Berinde, and M. Pacurar, Coupled fixed point theorems for generalized symmetric Meir-Keeler contractions in ordered metric spaces, Fixed Point Theory and Appl., 2012, 2012:115, doi:10.1186/1687-1812-2012-115] to a pair of mappings. We also give some applications of our main results.Article Citation - WoS: 7Citation - Scopus: 7On the Existence and Uniqueness of Solution of a Nonlinear Fractional Differential Equations(Eudoxus Press, Llc, 2013) Darzi, R.; Baleanu, Dumitru; Mohammadzadeh, B.; Neamaty, A.; Baleanu, D.; MatematikIn this paper, we investigate the existence and uniqueness of solution for fractional boundary value problem for nonlinear fractional differential equation D-0+(alpha) u(t) = f(t,u(t)), 0 < t < 1, 2 < alpha <= 3, with the integral boundary conditions {u(0) - gamma(1) u(1) = lambda(1) integral(1)(0) g(1) (s, u(s))ds, u'(0) - gamma(2)u'(1) = lambda(2) integral(1)(0) g(2) (s, u(s))ds, u ''(0) - gamma(2)u ''(1) = 0, where D-0+(alpha) denotes Caputo derivative of order alpha. by using the fixed point theory. We apply the contraction mapping principle and Krasnoselskii's fixed point theorem to obtain some new existence and uniqueness results. Two examples are given to illustrate the main results.Article Citation - WoS: 121Citation - Scopus: 125On Cauchy Problems With Caputo Hadamard Fractional Derivatives(Eudoxus Press, Llc, 2016) Jarad, Fahd; Adjabi, Y.; Baleanu, Dumitru; Jarad, Fahd; Baleanu, D.; Abdeljawad, Thabet; Abdeljawad, T.; MatematikThe current work is motivated by the so-called Caputo-type modification of the Hadamard or Caputo Hadamard fractional derivative discussed in [4]. The main aim of this paper is to study Cauchy problems for a differential equation with a left Caputo Hadamard fractional derivative in spaces of continuously differentiable functions. The equivalence of this problem to a nonlinear Volterra type integral equation of the second kind is shown. On the basis of the obtained results, the existence and uniqueness of the solution to the considered Cauchy problem is proved by using Banach's fixed point theorem. Finally, two examples are provided to explain the applications of the results.