Matematik Bölümü Yayın Koleksiyonu

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

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Publisher: search.filters.publisher.Amer inst Mathematical Sciences-aimsSubject: search.filters.subject.Boundary Value Problem

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Now showing 1 - 4 of 4
  • 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: 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.