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Browsing by Author "Ergoren, Hilmi"

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    Alternative Variational Iteration Method for Solving the Time-Fractional Fornberg-Whitham Equation
    (Elsevier Science inc, 2015) Sakar, Mehmet Giyas; Ergoren, Hilmi
    In this study, we apply an alternative variational iteration method to solve the time-fractional Fomberg-Whitham equation. A comparison between the results obtained using the alternative variational iteration method and known results obtained with the variational iteration method demonstrates that the proposed method is highly effective and convenient. The fractional derivatives are described in the Caputo sense. Numerical results are presented for different specific cases of the problem. (C) 2014 Elsevier Inc. All rights reserved.
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    Impulsive Fractional Differential Inclusions With Flux Boundary Conditions
    (Univ Nis, Fac Sci Math, 2017) Ergoren, Hilmi
    In this work we investigate some existence results for solutions of a boundary value problem for impulsive fractional differential inclusions supplemented with fractional flux boundary conditions by applying Bohnenblust-Karlin's fixed point theorem for multivalued maps.
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    Impulsive Functional Delay Differential Inclusions of Fractional Order at Variable Times
    (Springer, 2016) Ergoren, Hilmi
    We are concerned with some sufficient conditions for the existence of solutions of a class of initial value problems for impulsive fractional differential inclusions with functional delay at variable moments.
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    Non-Local Boundary Value Problems for Impulsive Fractional Integro-Differential Equations in Banach Spaces
    (Springeropen, 2012) Ergoren, Hilmi; Kilicman, Adem
    In this study, we establish some conditions for existence and uniqueness of the solutions to semilinear fractional impulsive integro-differential evolution equations with non-local conditions by using Schauder's fixed point theorem and the contraction mapping principle.
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    On Boundedness of a Certain Non-Linear Differential Equation of Third Order
    (Eudoxus Press, Llc, 2010) Tunc, Cemil; Ergoren, Hilmi
    This paper presents sufficient conditions for all solutions as well as their derivatives up to second order to x"' + a(t)f(x')x '' + b(t, x, x') +c(t)g(x) = et, x, x', x '') to be bounded. What is more, it shows that all the solutions are in L-p[0,infinity) Under somewhat more restrictive conditions.
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    On the Positive Solutions for Fractional Differential Equations With Weakly Contractive Mappings
    (Amer inst Physics, 2015) Ergoren, Hilmi
    This work aims to show the existence and uniqueness of positive solutions of a class of fractional differential equations subject to hybrid boundary conditions by using some fixed point theorems via weakly contractive maps in view of partially ordered sets.
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    Some Existence Results for Impulsive Nonlinear Fractional Differential Equations With Closed Boundary Conditions
    (Hindawi Ltd, 2012) Ergoren, Hilmi; Kilicman, Adem
    We investigate some existence results for the solutions to impulsive fractional differential equations having closed boundary conditions. Our results are based on contracting mapping principle and Burton-Kirk fixed point theorem.