Matematik Bölümü Yayın Koleksiyonu

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

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Scopus Q: search.filters.scopusQuartile.Q1Subject: search.filters.subject.Boundary Value Problem

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  • Article
    Citation - WoS: 10
    Citation - Scopus: 11
    Optimal Variational Iteration Method for Parametric Boundary Value Problem
    (Amer inst Mathematical Sciences-aims, 2022) Nadeem, Muhammad; Karim, Shazia; Akguel, Ali; Jarad, Fahd; Ain, Qura Tul; Akgül, Ali
    Mathematical applications in engineering have a long history. One of the most well-known analytical techniques, the optimal variational iteration method (OVIM), is utilized to construct a quick and accurate algorithm for a special fourth-order ordinary initial value problem. Many researchers have discussed the problem involving a parameter c. We solve the parametric boundary value problem that can't be addressed using conventional analytical methods for greater values of c using a new method and a convergence control parameter h. We achieve a convergent solution no matter how huge c is. For the approximation of the convergence control parameter h, two strategies have been discussed. The advantages of one technique over another have been demonstrated. Optimal variational iteration method can be seen as an effective technique to solve parametric boundary value problem.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 4
    A New Application of the Legendre Reproducing Kernel Method
    (Amer inst Mathematical Sciences-aims, 2022) Hashemi, Mir Sajjad; Gholizadeh, Leila; Akgul, Ali; Jarad, Fahd; Foroutan, Mohammad Reza
    In this work, we apply the reproducing kernel method to coupled system of second and fourth order boundary value problems. We construct a novel algorithm to acquire the numerical results of the nonlinear boundary-value problems. We also use the Legendre polynomials. Additionally, we discuss the convergence analysis and error estimates. We demonstrate the numerical simulations to prove the efficiency of the presented method.
  • Article
    Citation - WoS: 23
    Citation - Scopus: 26
    On the Boundary Value Problems of Hadamard Fractional Differential Equations of Variable Order
    (Wiley, 2023) Benkerrouche, Amar; Souid, Mohammed Said; Karapinar, Erdal; Hakem, Ali
    In this manuscript, we examine both the existence, uniqueness, and the stability of solutions to the boundary value problem (BVP) of Hadamard fractional differential equations of variable order by converting it into an equivalent standard Hadamard (BVP) of the fractional constant order with the help of the generalized intervals and the piecewise constant functions. All results in this study are established using Krasnoselskii fixed-point theorem and the Banach contraction principle. Further, the Ulam-Hyers stability of the given problem is examined, and finally, we construct an example to illustrate the validity of the observed results.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 14
    Novel 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, Hawsar
    This 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: 5
    Citation - Scopus: 3
    Nonlinear Fractional Differential Equations and Their Existence Via Fixed Point Theory Concerning To Hilfer Generalized Proportional Fractional Derivative
    (Amer inst Mathematical Sciences-aims, 2022) Ahmad, Abdulaziz Garba; Jarad, Fahd; Alsaadi, Ateq; Rashid, Saima
    This article adopts a class of nonlinear fractional differential equation associating Hilfer generalized proportional fractional (GPF) derivative with having boundary conditions, which amalgamates the Riemann-Liouville (RL) and Caputo-GPF derivative. Taking into consideration the weighted space continuous mappings, we first derive a corresponding integral for the specified boundary value problem. Also, we investigate the existence consequences for a certain problem with a new unified formulation considering the minimal suppositions on nonlinear mapping. Detailed developments hold in the analysis and are dependent on diverse tools involving Schauder's, Schaefer's and Kransnoselskii's fixed point theorems. Finally, we deliver two examples to check the efficiency of the proposed scheme.
  • Article
    Citation - WoS: 117
    Citation - Scopus: 120
    A Novel Modeling of Boundary Value Problems on the Glucose Graph
    (Elsevier, 2021) Etemad, Sina; Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, Dumitru
    In 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: 11
    Citation - Scopus: 11
    Some Singular Third-Order Boundary Value Problems
    (Wiley, 2020) Ugurlu, Ekin
    In this paper, we consider some singular formally symmetric (self-adjoint) boundary value problems generated by a singular third-order differential expression and separated and coupled boundary conditions. In particular, we consider that the minimal symmetric operator generated by the third-order differential expression has the deficiency indices (3,3). We investigate same spectral properties related with these problems, and we introduce a method to find the resolvent operator.
  • Article
    Citation - WoS: 15
    Citation - Scopus: 18
    Existence 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: 6
    Citation - Scopus: 7
    A Reliable Mixed Method for Singular Integro-Differential Equations of Non-Integer Order
    (Edp Sciences S A, 2018) Darzi, Rahmat; Agheli, Ahram; Baleanu, Dumitru; Agheli, Bahram
    It 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.
  • Article
    Citation - Scopus: 88
    Fractional Diffusion on Bounded Domains
    (Walter de Gruyter GmbH, 2015) D'Elia, M.; Du, Q.; Gunzburger, M.; Lehoucq, R.; Defterli, O.; Meerschaert, M.M.
    The mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. This paper discusses the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains. © 2015 Diogenes Co., Sofia.