Matematik Bölümü Yayın Koleksiyonu

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

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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: 13
    Citation - Scopus: 17
    Nonautonomous lump-periodic and analytical solutions tothe (3+1)-dimensional generalized Kadomtsev-Petviashviliequation
    (Springer, 2023) Alquran, Marwan; Sulaiman, Tukur Abdulkadir; Yusuf, Abdullahi; Alshomrani, Ali S.; Baleanu, Dumitru
    This work establishes the lump periodic and exact traveling wave solutions for the (3 + 1)-dimensional generalized Kadomtsev-Petviashvili equation. We use the Hirota bilinear method, as well as the robust integration techniques tanh-coth expansion and rational sine-cosine, to provide such innovative solutions. In order to explain specific physical difficulties, innovative lump periodic and analytical solutions have been investigated. These discoveries have been proven to be useful in the transmission of long-wave and high-power communications networks. It is important to highlight that the results given in thiswork depict new features and reflect previously unknown physical dynamics for the governing model.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    Existence and Hyers-Ulam Stability of Stochastic Integrodifferential Equations With a Random Impulse
    (Springer, 2023) Kasinathan, Ravikumar; Sandrasekaran, Varshini; Baleanu, Dumitru; Kasinathan, Ramkumar
    The theoretical approach of random impulsive stochastic integrodifferential equations (RISIDEs) with finite delay, noncompact semigroups, and resolvent operators in Hilbert space is investigated in this article. Initially, a random impulsive stochastic integrodifferential system is proposed and the existence of a mild solution for the system is established using the Monch fixed-point theorem and contemplating Hausdorff measures of noncompactness. Then, the stability results including a continuous dependence of solutions on initial conditions, exponential stability, and Hyers-Ulam stability for the aforementioned system are investigated. Finally, an example is proposed to validate the obtained results.
  • Article
    Citation - WoS: 18
    Citation - Scopus: 22
    Classes of Solitary Solution for Nonlinear Schrodinger Equation Arising in Optical Fibers and Their Stability Analysis
    (Springer, 2023) Baleanu, Dumitru; Ibrahim, Salisu
    In this work, we realised the soliton solutions of nonlinear Schrodinger equation (NLSE) that arise from optical fibers, we considered the modified Sardar sub-equation method (MSSEM) to find solitary solutions analytically. The stability of the retrieved soliton solutions realised from the NLSE are investigated. We demonstrate the soliton solutions that are stable and can last for a very long time without losing its form or energy under specific circumstances and those soliton solutions that are unstable. The MSSEM is a frequently employed technique in research for addressing specific mathematical modeling or physical phenomena problems. Its selection in this specific study might stem from its proven efficacy in handling the particular problem under investigation. The decision to utilize MSSEM could be driven by several considerations, including its precision, computationally efficient, effectiveness, greater accuracy and capability to manage intricate systems. Finally, our method offers greater flexibility in modeling various physical phenomena, which makes it particularly useful in applications in diverse fields such as quantum mechanics and nonlinear optics. The findings have ramifications for the architecture of optical fiber communications and offer significant new insights into the behavior of solitons in optical systems. The NLSE has proven to be an effective tool for understanding wave behavior in fiber optics. Its applications have helped engineers and scientists optimize the design of optical fibers and predict the behavior of various conditions. Moreover, our study provides insights into the fundamental properties of solitary solutions in the NLSEs and their practical implications in physical systems.
  • 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: 23
    Citation - Scopus: 23
    Abundant Optical Solitons To the (2+1)-Dimensional Kundu-Mukherjee Equation in Fiber Communication Systems
    (Springer, 2023) Baleanu, Dumitru; Ghanbari, Behzad
    The Kundu-Mukherjee-Naskar equation holds significant relevance as a nonlinear model for investigating intricate wave phenomena in fluid and optical systems. This study uncovers new optical soliton solutions for the KMN equation by employing analytical techniques that utilize combined elliptic Jacobian functions. The solutions exhibit mixtures of distinct Jacobian elliptic functions, offering novel insights not explored in prior KMN equation research. Visual representations in the form of 2D ContourPlots elucidate the physical behaviors and properties of these newly discovered solution forms. The utilization of symbolic computations facilitated the analytical derivation of these solutions, offering a deeper understanding of the nonlinear wave dynamics governed by the KMN equation. These employed techniques showcase the potential for future analytical advancements in unraveling the complex soliton landscape of the multifaceted KMN model. The findings provide valuable insights into the intricacies of soliton behavior within this nonlinear system, offering new perspectives for analysis and exploration in areas such as fiber optic communications, ocean waves, and fluid mechanics. Maple symbolic packages have enabled us to derive analytical results.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Some New Dynamic Inequalities With Several Functions of Hardy Type on Time Scales
    (Springer, 2021) Abuelela, Waleed; Saker, Samir H.; Baleanu, Dumitru; Hamiaz, Adnane
    The aim of this article is to prove some new dynamic inequalities of Hardy type on time scales with several functions. Our results contain some results proved in the literature, which are deduced as limited cases, and also improve some obtained results by using weak conditions. In order to do so, we utilize Holder's inequality, the chain rule, and the formula of integration by parts on time scales.
  • Article
    Citation - WoS: 11
    Citation - Scopus: 13
    Some New Dynamic Gronwall-Bellman Type Inequalities With Delay on Time Scales and Certain Applications
    (Springer, 2022) Baleanu, Dumitru; El-Deeb, Ahmed A.
    The main objective of the present article is to prove some new delay nonlinear dynamic inequalities of Gronwall-Bellman-Pachpatte type on time scales. We introduce very important generalized results with the help of Leibniz integral rule on time scales. For some specific time scales, we further show some relevant inequalities as special cases: integral inequalities and discrete inequalities. Our results can be used as handy tools for the study of qualitative and quantitative properties of solutions of dynamic equations on time scales. Some examples are provided to demonstrate the applications of the results.
  • Article
    Citation - WoS: 23
    Citation - Scopus: 23
    The Generalized Sasa-Satsuma Equation and Its Optical Solitons
    (Springer, 2022) Hosseini, K.; Sadri, K.; Salahshour, S.; Baleanu, D.; Mirzazadeh, M.; Inc, Mustafa
    The principal goal of the presented paper is to investigate the dynamics of optical solitons for the generalized Sasa-Satsuma (GSS) equation describing the propagation of the femtosecond pulses in the systems of optical fiber transmission. More precisely, the governing model, which is a generalized version of the classical Sasa-Satsuma equation, is firstly reduced in a one-dimensional real regime through a specific transformation; then, its bright and dark optical solitons are established using the modified Kudryashov (MK) method. The changes in the amplitude of the bright and dark solitons are analyzed as a case study for various classes of free parameters. Considerable changes are observed in the optical solitons amplitude from the results presented in the current study.
  • Article
    Citation - WoS: 15
    Citation - Scopus: 23
    Optical Solitons With Nonlinear Dispersion in Parabolic Law Medium and Three-Component Coupled Nonlinear Schrodinger Equation
    (Springer, 2022) Sulaiman, Tukur Abdulkadir; Alshomrani, Ali S.; Baleanu, Dumitru; Yusuf, Abdullahi
    The current study looks at two different nonlinear Schrodinger equations. These equations have several applications in science and engineering, such as nonlinear fiber optics, electromagnetic field waves, and signal processing via optical fibers. In this study, we investigate these equations using an efficient integration strategy known as complex envelop antazs. As a result, we obtain novel solutions such as bright, dark, and combined dark-bright soliton solutions. Important physical aspects have been depicted in three dimensions and contour plots for clear interpretation of the acquired solutions.