Matematik Bölümü Yayın Koleksiyonu

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

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Author: search.filters.author.Baleanu, DumitruSubject: search.filters.subject.Fixed Point

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Now showing 1 - 10 of 21
  • Article
    Citation - WoS: 4
    Citation - Scopus: 6
    A Fractional Derivative Inclusion Problem Via an Integral Boundary Condition
    (Eudoxus Press, Llc, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Moghaddam, Mehdi; Mohammadi, Hakimeh; Rezapour, Shahram; Matematik
    We 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 - Scopus: 3
    A Note on Sobolev Form Fractional Integro-Differential Equation With State-Dependent Delay Via Resolvent Operators
    (Cambridge Scientific Publishers, 2017) Mallika, D.; Baleanu, Dumitru; Suganya, S.; Baleanu, D.; Arjunan, M.M.; Matematik
    This paper explores the new existence and uniqueness of mild solutions for a class of Sobolev form fractional integro-differential equation (in short SFFIDE) with state-dependent delay (in short SDD) and nonlocal conditions (in short NLCs) via resolvent operators in Banach spaces. By making use of Banach contraction principle and Krasnoselskii fixed point theorem (in short FPT) along with resolvent operators and fractional calculus, we develop the sought outcomes. An illustration is furthermore provided to demonstrate the acquired concepts. © CSP - Cambridge, UK; I & S - Florida, USA, 2017.
  • Article
    Citation - WoS: 4
    Existence and Uniqueness of Solutions for a Nabla Fractional Boundary Value Problem With Discrete Mittag{leffler Kernel
    (inst Mathematics & Mechanics, Natl Acad Sciences Azerbaijan, 2021) Jonnalagadda, Jagan Mohan; Baleanu, Dumitru; Baleanu, Dumitru; Matematik
    We consider a two-point boundary-value problem of order 1 < alpha < 3/2 involving nabla fractional differences with discrete Mittag-Leffler kernels. In [2], the authors obtained an expression for the Green's function of this boundary value problem. We determine an upper bound for the Green's function and derive a Lyapunov-type inequality. Further, we also establish sufficient conditions on existence and uniqueness of solutions for the corresponding nonlinear problem using fixed point theorems.
  • Article
    Citation - Scopus: 1
    Existence Results for an Impulsive Pantograph Differential Equations Within Exponential Kernel
    (Univ Politehnica Bucharest, Sci Bull, 2022) Kavitha, Velusamy; Baleanu, Dumitru; Kanimozhi, Palanisamy; Arjunan, Mani Mallika; Baleanu, Dumitru; Matematik
    This manuscript deals with the existence results for an impulsive pantograph integro-differential equations (IPIDE) through Caputo-Fabrizio (CF) operator. Certain novel existence findings are shown using fixed point approaches. Finally, two numerical examples are provided in the work to demonstrate the application of our theoretical findings.
  • Article
    Citation - WoS: 22
    Citation - Scopus: 25
    New Approach on Controllability of Hilfer Fractional Derivatives With Nondense Domain
    (Amer inst Mathematical Sciences-aims, 2022) Jothimani, Kasthurisamy; Ravichandran, Chokkalingam; Baleanu, Dumitru; Kumar, Devendra; Nisar, Kottakkaran Sooppy
    This work picturizes the results on the controllability of the nondense Hilfer neutral fractional derivative (HNFD). The uniqueness and controllability of HNFD are discussed with Winch theorem and Banach contraction technique. In addition, a numerical approximation is given to deal with different criteria of our results.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 4
    Existence Results for Coupled Differential Equations of Non-Integer Order With Riemann-Liouville, Erdelyi-Kober Integral Conditions
    (Amer inst Mathematical Sciences-aims, 2021) Hemalatha, S.; Duraisamy, P.; Pandiyan, P.; Muthaiah, Subramanian; Baleanu, Dumitru
    This paper proposes the existence and uniqueness of a solution for a coupled system that has fractional differential equations through Erdelyi-Kober and Riemann-Liouville fractional integral boundary conditions. The existence of the solution for the coupled system by adopting the Leray-Schauder alternative. The uniqueness of solution for the problem can be found using Banach fixed point theorem. In order to verify the proposed criterion, some numerical examples are also discussed.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 3
    Controllability of Nonlocal Non-Autonomous Neutral Differential Systems Including Non-Instantaneous Impulsive Effects in R<sup>n</Sup>
    (Ovidius Univ Press, 2020) Arjunan, Mani Mallika; Baleanu, Dumitru; Kavitha, Velusamy
    This manuscript involves a class of first-order controllability results for nonlocal non-autonomous neutral differential systems with non-instantaneous impulses in the space R-n. Sufficient conditions guaranteeing the controllability of mild solutions are set up. Concept of evolution family and Rothe's fixed point theorem are employed to achieve the required results. A model is investigated to delineate the adequacy of the results.
  • Article
    Citation - WoS: 33
    Citation - Scopus: 37
    Approximation of Fixed Point and Its Application To Fractional Differential Equation
    (Springer Heidelberg, 2021) Uddin, Izhar; Baleanu, Dumitru; Khatoon, Sabiya
    In this study, we prove some convergence results for generalized alpha-Reich-Suzuki non-expansive mappings via a fast iterative scheme. We validate our result by constructing a numerical example. Also, we compare our results with the other well known iterative schemes. Finally, we calculate the approximate solution of nonlinear fractional differential equation.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 6
    Application of Some Special Operators on the Analysis of a New Generalized Fractional Navier Problem in the Context of Q-Calculus
    (Springer, 2021) Ntouyas, Sotiris K.; Imran, Atika; Hussain, Azhar; Baleanu, Dumitru; Rezapour, Shahram; Etemad, Sina
    The key objective of this study is determining several existence criteria for the sequential generalized fractional models of an elastic beam, fourth-order Navier equation in the context of quantum calculus (q-calculus). The required way to accomplish the desired goal is that we first explore an integral equation of fractional order w.r.t. q-RL-integrals. Then, for the existence of solutions, we utilize some fixed point and endpoint conditions with the aid of some new special operators belonging to operator subclasses, orbital alpha-admissible and alpha-psi-contractive operators and multivalued operators involving approximate endpoint criteria, which are constructed by using aforementioned integral equation. Furthermore, we design two examples to numerically analyze our results.
  • Article
    Analysis of the model of HIV-1 infection of CD4(+) T-cell with a new approach of fractional derivative
    (Springer, 2020) Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, Shahram
    By using the fractional Caputo-Fabrizio derivative, we investigate a new version for the mathematical model of HIV. In this way, we review the existence and uniqueness of the solution for the model by using fixed point theory. We solve the equation by a combination of the Laplace transform and homotopy analysis method. Finally, we provide some numerical analytics and comparisons of the results.