Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 5Citation - Scopus: 5Mild and Strong Solutions for a Fractional Nonlinear Neumann Boundary Value Problem(Eudoxus Press, Llc, 2013) Herzallah, Mohamed A. E.; Baleanu, Dumitru; El-Shahed, Moustafa; Baleanu, Dumitru; MatematikIn this paper, we investigated the following fractional Neumann boundary value problem D-C(0)alpha+u(t) - lambda u(t) = f (t, u(t)), u'(0) = u'(1) = 0, 1 < alpha < 2, lambda not equal 0, where D-C(a+)alpha is the fractional Caputo derivative. We proved the existence of at least one mild solution and we determined when this solution is unique for suitable assumptions on the function fArticle Citation - WoS: 3Citation - Scopus: 2Fractional Hybrid Initial Value Problem Featuring Q-Derivatives(Comenius Univ, 2019) Baleanu, D.; Baleanu, Dumitru; Darzi, R.; Agheli, B.; MatematikWe have perused about the existence of a solution toward hybrid initial value problem (HIVP) featuring fractional q-derivative {D-q(delta)[v(t)/h(t,v(t) max(0 <=tau <= t)vertical bar v(t)vertical bar] rho(t, v(t)), t is an element of(0,1), 0 < delta <= 1`, in which D-q(delta) denotes the Riemann-Liouville fractional q-derivative in the order of delta. In Banach algebra, by making use of a fi xed point theorem based Dhage along with mixed Lipschitz and Caratheodory condition, a way of solving the above fractional Hybrid initial value problem (FHIVP) featuring q-derivatives veri fi ed, in this study.Article Citation - WoS: 14Citation - Scopus: 14Novel Algorithms To Approximate the Solution of Nonlinear Integro-Differential Equations of Volterra-Fredholm Integro Type(Amer inst Mathematical Sciences-aims, 2023) Srivastava, Hari Mohan; Hama, Mudhafar; Mohammed, Pshtiwan Othman; Almusawa, Musawa Yahya; Baleanu, Dumitru; HamaRashid, HawsarThis study is devoted to examine the existence and uniqueness behavior of a nonlinear integro-differential equation of Volterra-Fredholm integral type in continues space. Then, we examine its solution by modification of Adomian and homotopy analysis methods numerically. Initially, the proposed model is reformulated into an abstract space, and the existence and uniqueness of solution is constructed by employing Arzela-Ascoli and Krasnoselskii fixed point theorems. Furthermore, suitable generation. At last, three test examples are presented to verify the established theoretical concepts.Article Citation - WoS: 15Citation - Scopus: 14Criteria for Existence of Solutions for a Liouville-Caputo Boundary Value Problem Via Generalized Gronwall's Inequality(Springer, 2021) Baleanu, Dumitru; Etemad, Sina; Rezapour, Shahram; Mohammadi, HakimehIn this research, we first investigate the existence of solutions for a new fractional boundary value problem in the Liouville-Caputo setting with mixed integro-derivative boundary conditions. To do this, Kuratowski's measure of noncompactness and Sadovskii's fixed point theorem are our tools to reach this aim. In the sequel, we discuss the continuous dependence of solutions on parameters by means of the generalized Gronwall inequality. Moreover, we consider an inclusion version of the given boundary problem in which we study its existence results by means of the endpoint theory. Finally, we prepare two simulative numerical examples to confirm the validity of the analytical findings.Article Citation - WoS: 27Citation - Scopus: 26Boundary Value Problem for Nonlinear Fractional Differential Equations of Variable Order Via Kuratowski Mnc Technique(Springer, 2021) Baleanu, Dumitru; Souid, Mohammed Said; Hakem, Ali; Inc, Mustafa; Benkerrouche, Amar; Said Souid, MohammedIn the present research study, for a given multiterm boundary value problem (BVP) involving the Riemann-Liouville fractional differential equation of variable order, the existence properties are analyzed. To achieve this aim, we firstly investigate some specifications of this kind of variable-order operators, and then we derive the required criteria to confirm the existence of solution and study the stability of the obtained solution in the sense of Ulam-Hyers-Rassias (UHR). All results in this study are established with the help of the Darbo's fixed point theorem (DFPT) combined with Kuratowski measure of noncompactness (KMNC). We construct an example to illustrate the validity of our observed results.Article Citation - WoS: 117Citation - Scopus: 120A Novel Modeling of Boundary Value Problems on the Glucose Graph(Elsevier, 2021) Etemad, Sina; Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, DumitruIn this article, with due attention to a new labeling method for vertices of arbitrary graphs, we investigate the existence results for a novel modeling of the fractional multi term boundary value problems on each edge of the graph representation of the Glucose molecule. In this direction, we consider a graph with labeled vertices by 0 or 1 inspired by the molecular structure of the Glucose molecule and then derive some existence results by applying two known fixed point theorems. Finally, we provide an example to illustrate the validity of our main result. (c) 2021 Elsevier B.V. All rights reserved.Article Citation - WoS: 6Citation - Scopus: 14A Subdivision-Based Approach for Singularly Perturbed Boundary Value Problem(Springer, 2020) Ejaz, Syeda Tehmina; Baleanu, Dumitru; Ghaffar, Abdul; Nisar, Kottakkaran Sooppy; Mustafa, GhulamA numerical approach for solving second order singularly perturbed boundary value problems (SPBVPs) is introduced in this paper. This approach is based on the basis function of a 6-point interpolatory subdivision scheme. The numerical results along with the convergence, comparison and error estimation of the proposed approach are also presented.Article Citation - WoS: 60Citation - Scopus: 65The Existence of Solutions for a Nonlinear Mixed Problem of Singular Fractional Differential Equations(Springer, 2013) Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, DumitruBy using fixed point results on cones, we study the existence of solutions for the singular nonlinear fractional boundary value problem (c)D(alpha)u(t) = f(t, u(t), u'(t), (c)D(beta)u(t)), u(0) = au(1), u'(0) = b(c)D(beta)u(1), u ''(0) = u'''(0) = u((n-1))(0) = 0, where n >= 3 is an integer, alpha is an element of (n - 1, n), 0 < beta < 1, 0 < a < 1, 0 < b < Gamma (2 - beta), f is an L-q-Caratheodory function, q > 1/alpha-1 and f(t,x,y,z) may be singular at value 0 in one dimension of its space variables x, y, z. Here, D-c stands for the Caputo fractional derivative.Article Citation - WoS: 15Citation - Scopus: 18Existence of a Periodic Mild Solution for a Nonlinear Fractional Differential Equation(Pergamon-elsevier Science Ltd, 2012) Baleanu, Dumitru; Herzallah, Mohamed A. E.; Mohammadzadeh, B.; Darzi, R.; Neamaty, A.The aim of this manuscript is to analyze the existence of a periodic mild solution to the problem of the following nonlinear fractional differential equation (R)(0)D(t)(alpha)u(t) - lambda u(t) = f(t, u(t)), u(0) = u(1) = 0, 1 < alpha < 2, lambda is an element of R, where D-R(0)t(alpha), denotes the Riemann-Liouville fractional derivative. We obtained the expressions of the general solution for the linear fractional differential equation by making use of the Laplace and inverse Laplace transforms. By making use of the Banach contraction mapping principle and the Schaefer fixed point theorem, the existence results of one or at least one mild solution for a nonlinear fractional differential equation were given. (C) 2011 Elsevier Ltd. All rights reserved.Article Citation - WoS: 6Citation - Scopus: 7A Reliable Mixed Method for Singular Integro-Differential Equations of Non-Integer Order(Edp Sciences S A, 2018) Darzi, Rahmat; Agheli, Ahram; Baleanu, Dumitru; Agheli, BahramIt is our goal in this article to apply a method which is based on the assumption that combines two methods of conjugating collocation and multiple shooting method. The proposed method can be used to find the numerical solution of singular fractional integro-differential boundary value problems (SFIBVPs) D-upsilon y(t) + eta integral(t)(0) (t - s)(zeta-1) y(s) ds = g(t), 1 < upsilon <= 2, 0 < zeta < 1, eta is an element of R, where D-upsilon denotes the Caputo derivative of order upsilon. Meanwhile, in a separate section the existence and uniqueness of this method is also discussed. Two examples are presented to illustrate the application and further understanding of the methods.