Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Now showing 1 - 10 of 16
  • Article
    Citation - WoS: 32
    Citation - Scopus: 33
    On the Multiparameterized Fractional Multiplicative Integral Inequalities
    (Springer, 2024) Saleh, Wedad; Lakhdari, Abdelghani; Jarad, Fahd; Meftah, Badreddine; Almatrafi, Mohammed Bakheet
    We introduce a novel multiparameterized fractional multiplicative integral identity and utilize it to derive a range of inequalities for multiplicatively s-convex mappings in connection with different quadrature rules involving one, two, and three points. Our results cover both new findings and established ones, offering a holistic framework for comprehending these inequalities. To validate our outcomes, we provide an illustrative example with visual aids. Furthermore, we highlight the practical significance of our discoveries by applying them to special means of real numbers within the realm of multiplicative calculus.
  • Article
    Citation - WoS: 22
    Citation - Scopus: 30
    Global Stability Results for Volterra-Hadamard Random Partial Fractional Integral Equations
    (Springer-verlag Italia Srl, 2023) Abbas, Said; Benchohra, Mouffak; Karapinar, Erdal; Salim, Abdelkrim
    This paper investigates the existence and stability of random solutions of a class of Hadamard fractional order functional partial integral equations with random effects in Banach spaces.
  • Article
    Citation - WoS: 6
    Citation - Scopus: 8
    Recovering the Space Source Term for the Fractional-Diffusion Equation With Caputo-Fabrizio Derivative
    (Springer, 2021) Nguyen Hoang Luc; Baleanu, Dumitru; Le Dinh Long; Le Nhat Huynh; Long, Le Dinh; Huynh, Le Nhat; Luc, Nguyen Hoang
    This article is devoted to the study of the source function for the Caputo-Fabrizio time fractional diffusion equation. This new definition of the fractional derivative has no singularity. In other words, the new derivative has a smooth kernel. Here, we investigate the existence of the source term. Through an example, we show that this problem is ill-posed (in the sense of Hadamard), and the fractional Landweber method and the modified quasi-boundary value method are used to deal with this inverse problem and the regularized solution is also obtained. The convergence estimates are addressed for the regularized solution to the exact solution by using an a priori regularization parameter choice rule and an a posteriori parameter choice rule. In addition, we give a numerical example to illustrate the proposed method.
  • Article
    Citation - WoS: 12
    Citation - Scopus: 15
    On the Weighted Fractional Integral Inequalities for Chebyshev Functionals
    (Springer, 2021) Nisar, Kottakkaran Sooppy; Khan, Sami Ullah; Baleanu, Dumitru; Vijayakumar, V.; Rahman, Gauhar
    The goal of this present paper is to study some new inequalities for a class of differentiable functions connected with Chebyshev's functionals by utilizing a fractional generalized weighted fractional integral involving another function G in the kernel. Also, we present weighted fractional integral inequalities for the weighted and extended Chebyshev's functionals. One can easily investigate some new inequalities involving all other type weighted fractional integrals associated with Chebyshev's functionals with certain choices of omega(theta) and G(theta) as discussed in the literature. Furthermore, the obtained weighted fractional integral inequalities will cover the inequalities for all other type fractional integrals such as Katugampola fractional integrals, generalized Riemann-Liouville fractional integrals, conformable fractional integrals and Hadamard fractional integrals associated with Chebyshev's functionals with certain choices of omega(theta) and G(theta).
  • Article
    Citation - WoS: 42
    Citation - Scopus: 51
    On Hyers-Ulam Mittag-Leffler Stability of Discrete Fractional Duffing Equation With Application on Inverted Pendulum
    (Springer, 2020) Baleanu, D.; Alzabut, J.; Vignesh, D.; Abbas, S.; Selvam, A. G. M.
    A human being standing upright with his feet as the pivot is the most popular example of the stabilized inverted pendulum. Achieving stability of the inverted pendulum has become common challenge for engineers. In this paper, we consider an initial value discrete fractional Duffing equation with forcing term. We establish the existence, Hyers-Ulam stability, and Hyers-Ulam Mittag-Leffler stability of solutions for the equation. We consider the inverted pendulum modeled by Duffing equation as an example. The values are tabulated and simulated to show the consistency with theoretical findings.
  • Article
    Citation - WoS: 56
    Citation - Scopus: 67
    On Hilfer Generalized Proportional Fractional Derivative
    (Springer, 2020) Kumam, Poom; Jarad, Fahd; Borisut, Piyachat; Jirakitpuwapat, Wachirapong; Ahmed, Idris
    Motivated by the Hilfer and the Hilfer-Katugampola fractional derivative, we introduce in this paper a new Hilfer generalized proportional fractional derivative, which unifies the Riemann-Liouville and Caputo generalized proportional fractional derivative. Some important properties of the proposed derivative are presented. Based on the proposed derivative, we consider a nonlinear fractional differential equation with nonlocal initial condition and show that this equation is equivalent to the Volterra integral equation. In addition, the existence and uniqueness of solutions are proven using fixed point theorems. Furthermore, we offer two examples to clarify the results.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    On a Kirchhoff Diffusion Equation With Integral Condition
    (Springer, 2020) Baleanu, Dumitru; Nguyen Hoang Luc; Nguyen Huu Can; Danh Hua Quoc Nam; Nam, Danh Hua Quoc; Luc, Nguyen Hoang; Can, Nguyen Huu
    This paper is devoted to Kirchhoff-type parabolic problem with nonlocal integral condition. Our problem has many applications in modeling physical and biological phenomena. The first part of our paper concerns the local existence of the mild solution in Hilbert scales. Our results can be studied into two cases: homogeneous case and inhomogeneous case. In order to overcome difficulties, we applied Banach fixed point theorem and some new techniques on Sobolev spaces. The second part of the paper is to derive the ill-posedness of the mild solution in the sense of Hadamard.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Nonexistence Results of Caputo-Type Fractional Problem
    (Springer, 2021) Ali, Saeed M.; Abdo, Mohammed S.; Jarad, Fahd; Kassim, Mohammed D.
    In this paper, we deal with Caputo-type fractional differential inequality where there is a low-order fractional derivative with the term polynomial source. We investigate the nonexistence of nontrivial global solutions in a suitable space via the test function technique and some properties of fractional integrals. Finally, we demonstrate three examples to illustrate our results. The presented results are more general than those in the literature, which can be obtained as particular cases.
  • Article
    Citation - WoS: 9
    Citation - Scopus: 12
    Existence Theory and Approximate Solution To Prey-Predator Coupled System Involving Nonsingular Kernel Type Derivative
    (Springer, 2020) Eiman; Shah, Kamal; Jarad, Fahd; Al-Mdallal, Qasem; Alqudah, Manar A.; Abdeljawad, Thabet
    This manuscript considers a nonlinear coupled system under nonsingular kernel type derivative. The considered problem is investigated from two aspects including existence theory and approximate analytical solution. For the concerned qualitative theory, some fixed point results are used. While for approximate solution, the Laplace transform coupled with Adomian method is applied. Finally, by a pertinent example of prey-predator system, we support our results. Some graphical presentations are given using Matlab.
  • Article
    Citation - WoS: 27
    Citation - Scopus: 26
    Boundary 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, Mohammed
    In 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.