WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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Author: search.filters.author.Jarad, FahdPublisher: search.filters.publisher.Springer

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Now showing 1 - 10 of 42
  • Article
    Citation - WoS: 51
    Citation - Scopus: 66
    Existence and Uniqueness of Solutions to Fractional Differential Equations in the Frame of Generalized Caputo Fractional Derivatives
    (Springer, 2018) Gambo, Y. Y.; Ameen, R.; Jarad, Fahd; Abdeljawad, T.
    The generalized Caputo fractional derivative is a name attributed to the Caputo version of the generalized fractional derivative introduced in Jarad et al. (J. Nonlinear Sci. Appl. 10:2607-2619, 2017). Depending on the value of. in the limiting case, the generality of the derivative is that it gives birth to two different fractional derivatives. However, the existence and uniqueness of solutions to fractional differential equations with generalized Caputo fractional derivatives have not been proven. In this paper, Cauchy problems for differential equations with the above derivative in the space of continuously differentiable functions are studied. Nonlinear Volterra type integral equations of the second kind corresponding to the Cauchy problem are presented. Using Banach fixed point theorem, the existence and uniqueness of solution to the considered Cauchy problem is proven based on the results obtained.
  • Article
    Citation - WoS: 13
    Citation - Scopus: 11
    An Expanded Analysis of Local Fractionalintegral Inequalities Via Generalized (s,p)-Convexity
    (Springer, 2024) Li, Hong; Lakhdari, Abdelghani; Jarad, Fahd; Xu, Hongyan; Meftah, Badreddine
    This research aims to scrutinize specific parametrized integral inequalities linked to 1,2, 3, and 4-point Newton-Cotes rules applicable to local fractional differentiable generalized (s,P)-convex functions. To accomplish this objective, we introduce a novel integral identity and deduce multiple integral inequalities tailored to mappings within the aforementioned function class. Furthermore, we present an illustrative example featuring graphical representations and potential practical applications.
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  • 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: 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: 7
    Citation - Scopus: 7
    On Boundary Value Problems of Caputo Fractional Differential Equation of Variable Order Via Kuratowski Mnc Technique
    (Springer, 2022) Souid, Mohammed Said; Hakem, Ali; Jarad, Fahd; Benkerrouche, Amar
    In this manuscript, we examine both the existence and the stability of solutions to the boundary value problem of Caputo fractional differential equations of variable order by converting it into an equivalent standard Caputo boundary value problem of the fractional constant order with the help of the generalized intervals and the piece-wise constant functions. All results in this study are established using Darbo's fixed point theorem combined with the Kuratowski measure of noncompactness. 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: 41
    Citation - Scopus: 51
    Non-Linear Soliton Solutions of Perturbed Chen-Lee Model by Φ<sup>6</Sup> -Model Expansion Approach
    (Springer, 2022) Asjad, Muhammad Imran; Jarad, Fahd; Faridi, Waqas Ali
    This study deals with the perturbed Chen-Lee-Liu governing mode which portrays the propagating phenomena of the optical pulses in the discipline of optical fiber and plasma. The Cauchy problem for this equation cannot be solved by the inverse scattering transform and we use an analytical approach to find traveling wave solutions. One of the generalized techniques phi(6) -model expansion method is exerted to find new solitary wave profiles. It is an effective, and reliable technique that provides generalized solitonic wave profiles including numerous types of soliton families. As a result, solitonic wave patterns attain, like Jacobi elliptic function, periodic, dark, bright, singular, dark-bright, exponential, trigonometric, and rational solitonic structures, etc. The constraint corresponding to each obtained solution provides the guarantee of the existence of the solitary wave solutions. The graphical 2-D, 3-D, and contour visualization of the obtained results is presented to express the pulse propagation behaviors by assuming the appropriate values of the involved parameters. The phi(6) -model expansion method is simple which can be easily applied to other complex non-linear models and get solitary wave structures.
  • Article
    Citation - WoS: 10
    Citation - Scopus: 13
    Existence and Uniqueness Results for Φ-Caputo Implicit Fractional Pantograph Differential Equation With Generalized Anti-Periodic Boundary Condition
    (Springer, 2020) Abdeljawad, Thabet; Jarad, Fahd; Borisut, Piyachat; Demba, Musa Ahmed; Kumam, Wiyada; Ahmed, Idris; Kumam, Poom
    The present paper describes the implicit fractional pantograph differential equation in the context of generalized fractional derivative and anti-periodic conditions. We formulated the Green's function of the proposed problems. With the aid of a Green's function, we obtain an analogous integral equation of the proposed problems and demonstrate the existence and uniqueness of solutions using the techniques of the Schaefer and Banach fixed point theorems. Besides, some special cases that show the proposed problems extend the current ones in the literature are presented. Finally, two examples were given as an application to illustrate the results obtained.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 7
    Estimates for P-Adic Fractional Integral Operator and Its Commutators on P-Adic Morrey-Herz Spaces
    (Springer, 2022) Aslam, Muhammad; Zaman, Mir; Jarad, Fahd; Sarfraz, Naqash
    This research investigates the boundedness of a p-adic fractional integral operator on p-adic Morrey-Herz spaces. In particular, p-adic central bounded mean oscillations (C(M)over dotO) and Lipschitz estimate for commutators of the p-adic fractional integral operator are provided as well.
  • Article
    Citation - Scopus: 1
    Revisiting Generalized Caputo Derivatives in the Context of Two-Point Boundary Value Problems With the P-Laplacian Operator at Resonance
    (Springer, 2023) Jarad, Fahd; Bouloudene, Mokhtar; Panda, Sumati Kumari; Adjabi, Yassine
    The novelty of this paper is that, based on Mawhin's continuation theorem, we present some sufficient conditions that ensure that there is at least one solution to a particular kind of a boundary value problem with the p-Laplacian and generalized fractional Caputo derivative.