Matematik Bölümü Yayın Koleksiyonu

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

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Publication Index: search.filters.publicationIndex.ScopusSubject: search.filters.subject.Boundary Value Problem

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  • Article
    Citation - WoS: 6
    Citation - Scopus: 6
    A Caputo Fractional Order Boundary Value Problem With Integral Boundary Conditions
    (Eudoxus Press, Llc, 2013) Babakhani, Azizollah; Abdeljawad, Thabet; Abdeljawad, Thabet; Matematik
    In this paper, we discuss existence and uniqueness of solutions to nonlinear fractional order ordinary differential equations with integral boundary conditions in an ordered Banach space. We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function. The nonlinear alternative of the Leray- Schauder type Theorem is the main tool used here to establish the existence and the Banach contraction principle to show the uniqueness of the solution under certain conditions. The compactness of solutions set is also investigated and an example is included to show the applicability of our results.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    Mild 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; Matematik
    In 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 f
  • Article
    Citation - WoS: 3
    Citation - Scopus: 2
    Fractional Hybrid Initial Value Problem Featuring Q-Derivatives
    (Comenius Univ, 2019) Baleanu, D.; Baleanu, Dumitru; Darzi, R.; Agheli, B.; Matematik
    We 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
    Quasilinear Coupled System in the Frame of Nonsingular Abc-Derivatives With P-Laplacian Operator at Resonance
    (Springer Basel Ag, 2024) Jarad, Fahd; Adjabi, Yassine; Panda, Sumati Kumari; Bouloudene, Mokhtar
    We investigate the existence of solutions for coupled systems of fractional p-Laplacian quasilinear boundary value problems at resonance given by the Atangana-Baleanu-Caputo (shortly, ABC) derivatives formulations are based on the well-known Mittag-Leffler kernel utilizing Ge's application of Mawhin's continuation theorem. Examples are provided to demonstrate our findings.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 14
    Boundary Value Problem of Weighted Fractional Derivative of a Function With a Respect To Another Function of Variable Order
    (Springer, 2023) Jarad, Fahd; Alqudah, Manar A.; Abdeljawad, Thabet; Benia, Kheireddine; Souid, Mohammed Said
    This study aims to resolve weighted fractional operators of variable order in specific spaces. We establish an investigation on a boundary value problem of weighted fractional derivative of one function with respect to another variable order function. It is essential to keep in mind that the symmetry of a transformation for differential equations is connected to local solvability, which is synonymous with the existence of solutions. As a consequence, existence requirements for weighted fractional derivative of a function with respect to another function of constant order are necessary. Moreover, the stability with in Ulam-Hyers-Rassias sense is reviewed. The outcomes are derived using the Kuratowski measure of non-compactness. A model illustrates the trustworthiness of the observed results.
  • 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.