Article
Mathematics, Applied
Yingjie Liang, Yue Yu, Richard L. Magin
Summary: This study proposes a conversion method to compute the inverse Mittag-Leffler function and shows that it can capture ultraslow dynamics in various systems.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2022)
Article
Mathematics, Applied
Aqeel Ahmad, Cicik Alfiniyah, Ali Akgul, Aeshah A. Raezah
Summary: This study investigates the spread of COVID-19 in the Democratic Republic of the Congo using fractional operators, with the epidemic scenario in the country as a case study. It validates the existence and positivity of the epidemic problem and demonstrates unique solutions through the application of fixed-point theory. The study also uses advanced methodologies to examine the impact of COVID-19 on different age groups and provides numerical simulations to illustrate the behavior of the infectious disease.
Article
Optics
K. El Anouz, C. P. Onyenegecha, A. Opara, Ahmed Salah, A. El Allati
Summary: This paper presents an exact general solution to the fractional Schrodinger equation of two interacting atoms and investigates the influence of phase parameter and quantum coherence on quantum Fisher information. The analytical results demonstrate the similarity between these measures for certain critical values of the phase parameter.
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS
(2022)
Article
Materials Science, Multidisciplinary
Muhammad Farman, Maryam Batool, Kottakkaran Sooppy Nisar, Abdul Sattar Ghaffari, Aqeel Ahmad
Summary: This research proposes a mathematical model of cancer treatment with chemotherapy using a fractal fractional Mittag-Leffler operator with non-integer order. The model is analyzed both qualitatively and quantitatively. The control of cancer treatment with chemotherapy effects is established using a fractal fractional operator with a Mittag-Leffler kernel and control theory.
RESULTS IN PHYSICS
(2023)
Article
Mathematics, Applied
V. V. Saenko
Summary: The paper discusses the calculation of the Mittag-Leffler function E-rho,E-mu(z) by transforming integral representations in a way that eliminates complex variables and parameters. The accuracy of the new integral representations is verified by comparing the results with known representations of the Mittag-Leffler function.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2022)
Article
Mathematics
Farah Suraya Md Nasrudin, Chang Phang
Summary: In this work, the operational matrix based on shifted Legendre polynomials is applied to solve Prabhakar fractional differential equations. By transforming the equations into a system of algebraic equations, the numerical solution can be obtained with a few terms of shifted Legendre polynomials, ensuring accurate results.
JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics, Applied
Oscar Martinez-Fuentes, Guillermo Fernandez-Anaya, Aldo Jonathan Munoz-Vazquez
Summary: Stability analysis is crucial in control systems design. This paper focuses on fractional systems modeled by the Atangana-Baleanu derivative, introducing novel inequalities and considering quadratic and convex Lyapunov functions for stability analysis using the Direct Lyapunov Method.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Interdisciplinary Applications
Nicos Makris
Summary: This passage discusses the relationship between the memory function and creep compliance of complex materials, as well as the relationship between the fractional derivative of the Dirac delta function and the inverse Laplace transform. It also explores the singularities produced by the fractional derivative of the Rabotnov function and the extraction of finite number of fractional derivatives of the Dirac delta function.
FRACTAL AND FRACTIONAL
(2021)
Article
Engineering, Mechanical
Oscar Martinez-Fuentes, Aldo Jonathan Munoz-Vazquez, Guillermo Fernandez-Anaya, Esteban Tlelo-Cuautle
Summary: In this paper, a class of dynamic observers for nonlinear fractional-order systems is studied, and the Mittag-Leffler stability is analyzed. The Riemann-Liouville integral is utilized to provide robustness against noisy measurements, and a family of high gain proportional rho-integral observers is designed for estimating unmeasured state variables.
NONLINEAR DYNAMICS
(2023)
Article
Automation & Control Systems
Zhang Zhe, Wang Yaonan, Zhang Jing, Zhaoyang Ai, FanYong Cheng, Feng Liu
Summary: A novel decentralized non-integer order controller is proposed for nonlinear fractional-order composite systems (NFOCS), and some novel results for asymptotic stabilization are shown. The controller provides a solution for the asymptotic stabilization problem of NFOCS and has a wider control gain range with weaker requirements.
Article
Mathematics, Applied
Churong Chen
Summary: This paper considers discrete Caputo delta fractional economic cobweb models and discusses the properties of discrete Mittag-Leffler functions and stability conditions for solution of fractional difference equations. The conclusions are summarized with a numerical example.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2023)
Article
Mathematics, Interdisciplinary Applications
Ferhan M. Atici, Samuel Chang, Jagan Mohan Jonnalagadda
Summary: In this paper, an efficient method is proposed to calculate the values of the Mittag-Leffler (h-ML) function in discrete time hN. A matrix equation is constructed to represent an iteration scheme derived from a fractional h-difference equation with an initial condition. Fractional h-discrete operators are defined using the Nabla operator and the Riemann-Liouville definition. Figures and examples are provided to demonstrate this new calculation technique for the h-ML function in discrete time. Additionally, the h-ML function with a square matrix variable in a square matrix form is presented after proving the Putzer algorithm.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Mohammed Al-Refai, Dumitru Baleanu
Summary: This short paper suggests an extension of the fractional operator involving the Mittag-Leffler kernel to deal with non-singular kernels, which allows for integrable singular kernels at the origin. New solutions to related differential equations are reported, along with some perspectives from a modeling viewpoint.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics, Applied
Berat Karaagac, Kolade M. Owolabi
Summary: The study aims to analyze and obtain a new numerical approach for polio, an important mathematical model. By using noninteger-order derivative modeling, the study finds that the model is more accurate and reliable. A new numerical approximation method is proposed and validated through experiments.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Nanoscience & Nanotechnology
Chen Yue, Miao Peng, M. Higazy, Mostafa M. A. Khater
Summary: Analytical and semi-analytical soliton solutions for the nonlinear fractional (2 + 1)-dimensional integrable Calogero-Bogoyavlenskii-Schiff equation (FCBSE) in non-local form were obtained using recent computational and numerical methods. The FCBSE is an important model for studying various phenomena such as internal ocean waves, tsunamis, river tidal waves, and magneto-sound waves in plasma. The constructed solutions help understand the interaction between a long wave moving along the x-axis and a Riemann wave propagating along the y-axis. Different analytical solutions have been formulated for this model based on exponential, trigonometric, and hyperbolic functions, which are specific derivations of the well-known Korteweg-de Vries equation. Density charts are used to visualize the behavior of a single soliton through simulations. The results demonstrate the effectiveness of the numerical scheme and methods used in this study, showing the potential of recent computational and numerical techniques in solving nonlinear mathematical and physical problems.
