WoS İndeksli Yayınlar Koleksiyonu

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

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Now showing 1 - 10 of 81
  • Article
    Citation - WoS: 3
    Citation - Scopus: 4
    Monotonicity Results for Nabla Riemann-Liouville Fractional Differences
    (Mdpi, 2022) Mohammed, Pshtiwan Othman; Srivastava, Hari Mohan; Balea, Itru; Jan, Rashid; Abualnaja, Khadijah M.; Baleanu, Dumitru
    Positivity analysis is used with some basic conditions to analyse monotonicity across all discrete fractional disciplines. This article addresses the monotonicity of the discrete nabla fractional differences of the Riemann-Liouville type by considering the positivity of ((RL)(b0)del(theta)g)(z) combined with a condition on g(b(0)+2), g(b(0)+3) and g(b(0)+4), successively. The article ends with a relationship between the discrete nabla fractional and integer differences of the Riemann-Liouville type, which serves to show the monotonicity of the discrete fractional difference ((RL)(b0)del(theta)g)(z).
  • Article
    The Hausdorff-Pompeiu Distance in Gn-Menger Fractal Spaces
    (Mdpi, 2022) Saadati, Reza; Li, Chenkuan; Jarad, Fahd; O'Regan, Donal; O’Regan, Donal
    This paper introduces a complete Gn-Menger space and defines the Hausdorff-Pompeiu distance in the space. Furthermore, we show a novel fixed-point theorem for Gn-Menger-theta-contractions in fractal spaces.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 5
    On Transformation Involving Basic Analogue To the Aleph-Function of Two Variables
    (Mdpi, 2022) Baleanu, Dumitru; Ayant, Frederic; Suedland, Norbert; Kumar, Dinesh; Südland, Norbert
    In our work, we derived the fractional order q-integrals and q-derivatives concerning a basic analogue to the Aleph-function of two variables (AFTV). We discussed a related application and the q-extension of the corresponding Leibniz rule. Finally, we presented two corollaries concerning the basic analogue to the I-function of two variables and the basic analogue to the Aleph-function of one variable.
  • Article
    Citation - WoS: 19
    Citation - Scopus: 23
    On the Solvability of Mixed-Type Fractional-Order Non-Linear Functional Integral Equations in the Banach Space C(I)
    (Mdpi, 2022) Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Baleanu, Dumitru; Pathak, Vijai Kumar
    This paper is concerned with the existence of the solution to mixed-type non-linear fractional functional integral equations involving generalized proportional (kappa,phi)-Riemann-Liouville along with Erdelyi-Kober fractional operators on a Banach space C([1,T]) arising in biological population dynamics. The key findings of the article are based on theoretical concepts pertaining to the fractional calculus and the Hausdorff measure of non-compactness (MNC). To obtain this goal, we employ Darbo's fixed-point theorem (DFPT) in the Banach space. In addition, we provide two numerical examples to demonstrate the applicability of our findings to the theory of fractional integral equations.
  • Article
    Citation - WoS: 27
    Citation - Scopus: 28
    On Dynamic Systems in the Frame of Singular Function Dependent Kernel Fractional Derivatives
    (Mdpi, 2019) Jarad, Fahd; Sene, Ndolane; Abdeljawad, Thabet; Madjidi, Fadila
    In this article, we discuss the existence and uniqueness theorem for differential equations in the frame of Caputo fractional derivatives with a singular function dependent kernel. We discuss the Mittag-Leffler bounds of these solutions. Using successive approximation, we find a formula for the solution of a special case. Then, using a modified Laplace transform and the Lyapunov direct method, we prove the Mittag-Leffler stability of the considered system.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 6
    New Solutions of Nonlinear Dispersive Equation in Higher-Dimensional Space With Three Types of Local Derivatives
    (Mdpi, 2022) Hashemi, Mir Sajjad; Jarad, Fahd; Akgul, Ali
    The aim of this paper is to use the Nucci's reduction method to obtain some novel exact solutions to the s-dimensional generalized nonlinear dispersive mK(m,n) equation. To the best of the authors' knowledge, this paper is the first work on the study of differential equations with local derivatives using the reduction technique. This higher-dimensional equation is considered with three types of local derivatives in the temporal sense. Different types of exact solutions in five cases are reported. Furthermore, with the help of the Maple package, the solutions found in this study are verified. Finally, several interesting 3D, 2D and density plots are demonstrated to visualize the nonlinear wave structures more efficiently.
  • Article
    Citation - WoS: 22
    Citation - Scopus: 22
    Lump Collision Phenomena To a Nonlinear Physical Model in Coastal Engineering
    (Mdpi, 2022) Yusuf, Abdullahi; Alshomrani, Ali Saleh; Baleanu, Dumitru; Sulaiman, Tukur Abdulkadir
    In this study, a dimensionally nonlinear evolution equation, which is the integrable shallow water wave-like equation, is investigated utilizing the Hirota bilinear approach. Lump solutions are achieved by its bilinear form and are essential solutions to various kind of nonlinear equations. It has not yet been explored due to its vital physical significant in various field of nonlinear science. In order to establish some more interaction solutions with some novel physical features, we establish collision aspects between lumps and other solutions by using trigonometric, hyperbolic, and exponential functions. The obtained novel types of results for the governing equation includes lump-periodic, two wave, and breather wave solutions. Meanwhile, the figures for these results are graphed. The propagation features of the derived results are depicted. The results reveal that the appropriate physical quantities and attributes of nonlinear waves are related to the parameter values.
  • Article
    Citation - WoS: 27
    Citation - Scopus: 30
    Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid With Newtonian Heating: Prabhakar Fractional Derivative Approach
    (Mdpi, 2022) Jarad, Fahd; Riaz, Muhammad Bilal; Shah, Zaheer Hussain; Rehman, Aziz Ur
    In this article, the effects of Newtonian heating along with wall slip condition on temperature is critically examined on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer Maxwell fluid near an infinitely vertical plate under constant concentration. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on a newly introduced Prabhakar fractional operator with generalized Fourier's law and Fick's law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration, and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as <mml:semantics>alpha</mml:semantics>, <mml:semantics>Pr</mml:semantics>, <mml:semantics>beta</mml:semantics>, <mml:semantics>Sc</mml:semantics>, <mml:semantics>Gr</mml:semantics>, <mml:semantics>gamma</mml:semantics>, and <mml:semantics>Gm</mml:semantics> are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical Maxwell model, classical Newtonian model, and fractional Newtonian model are recovered from Prabhakar fractional Maxwell fluid. Moreover, we compare the results between Maxwell and Newtonian fluids for both fractional and classical cases with and without slip conditions, showing that the movement of the Maxwell fluid is faster than viscous fluid. Additionally, it is visualized that both classical Maxwell and viscous fluid have relatively higher velocity as compared to fractional Maxwell and viscous fluid.
  • Article
    Citation - WoS: 20
    Citation - Scopus: 21
    Fractional Order Mathematical Model of Serial Killing With Different Choices of Control Strategy
    (Mdpi, 2022) Ahmad, Shabir; Arfan, Muhammad; Akgul, Ali; Jarad, Fahd; Rahman, Mati Ur
    The current manuscript describes the dynamics of a fractional mathematical model of serial killing under the Mittag-Leffler kernel. Using the fixed point theory approach, we present a qualitative analysis of the problem and establish a result that ensures the existence of at least one solution. Ulam's stability of the given model is presented by using nonlinear concepts. The iterative fractional-order Adams-Bashforth approach is being used to find the approximate solution. The suggested method is numerically simulated at various fractional orders. The simulation is carried out for various control strategies. Over time, all of the compartments demonstrate convergence and stability. Different fractional orders have produced an excellent comparison outcome, with low fractional orders achieving stability sooner.
  • Article
    Citation - WoS: 10
    Citation - Scopus: 10
    Fixed-Point Results for Meir-Keeler Type Contractions in Partial Metric Spaces: a Survey
    (Mdpi, 2022) Agarwal, Ravi P.; Yesilkaya, Seher Sultan; Wang, Chao; Karapinar, Erdal
    In this paper, we aim to review Meir-Keeler contraction mappings results on various abstract spaces, in particular, on partial metric spaces, dislocated (metric-like) spaces, and M-metric spaces. We collect all significant results in this direction by involving interesting examples. One of the main reasons for this work is to help young researchers by giving a framework for Meir Keeler's contraction.