关于与一般化的米塔格-莱弗勒函数相关的概括式-分数导数和积分运算符
Hira Khan1, Gauhar Rahman1, Muhammad Samraiz2
1Department of Mathematics and Statistics, Hazara University, Mansehra, 21300, Pakistan.
Heliyon
|March 3, 2025
概括
这项研究引入了使用三参数米塔格-莱弗勒函数的泛式分数-分数 (GFF) 运算符,为复杂现象建模提供了比现有的阿坦加纳-巴莱努和卡普托-法布里齐奥衍生品更普遍的方法.
科学领域:
- 数学 数学 是一个数学.
- 分数微积分的计算.
- 非整数的订单计算.
背景情况:
- 广泛应用的是Atangana-Baleanu (AB) 和Caputo Fabrizio (CF) 分数-分数导数,利用一个参数的米塔格-莱弗勒函数.
- 现有的运算符尚未被探索为三参数的米塔格-莱弗勒函数.
- 需要更普遍的运算符来建模复杂的动态.
研究的目的:
- 定义和研究一个全新的类型的概括式分数-分数 (GFF) 微分和积分运算符.
- 为了将修改的三参数米塔格-勒弗勒函数纳入碎形微积分计算.
- 扩大分数-分数运算符的适用性,用于模拟自然和物理现象.
主要方法:
- 开发具有一般化米塔格-莱弗勒核的一般化分 ভগ্নাংশ-分 ভগ্নাংশ (GFF) 微分和积分运算符.
- 修改现有的卡普托·法布里齐奥 (CF),阿坦加纳-巴莱努 (AB) 和一般化的哈塔夫分数-分数 (GHF) 运算符.
- 对新的GFF运营商进行分析和图形分析,包括与现有方法进行比较.
主要成果:
- 引入一个新的类型的概括加权分数-分数运算符.
- 用一个示例应用来展示GFF运营商模拟复杂动态的能力.
- 为新运营商展示新的分析和图形结果.
- 在特定的参数条件下恢复传统运营商.
结论:
- 新定义的GFF运营商与现有的分数-分数运营商相比,代表了更广泛的框架.
- 采用一般化的Mittag-Leffler内核的GFF操作员为复杂系统建模提供了增强的能力.
- 该研究为进一步研究高级分数-分数微积分应用提供了基础.
相关概念视频
Second Derivatives and Laplace Operator
1.2K
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
Consider a scalar function. The curl of its...
1.2K
Gradient and Del Operator
2.5K
In mathematics and physics, the gradient and del operator are fundamental concepts used to describe the behavior of functions and fields in space. The gradient is a mathematical operator that gives both the magnitude and direction of the maximum spatial rate of change. Consider a person standing on a mountain. The slope of the mountain at any given point is not defined unless it is quantified in a particular direction. For this reason, a "directional derivative" is defined, which is a vector...
2.5K
Properties of Laplace Transform-II
164
Time differentiation, convolution, integration, and periodicity are fundamental concepts in analyzing functions and signals over time. Each concept provides a unique perspective on how functions evolve, interact, and repeat, offering essential tools for various scientific and engineering applications.
Time differentiation involves analyzing the rate of change of a function over time. Mathematically, it is the derivative of a function with respect to time. This concept can be likened to tracking...
Time differentiation involves analyzing the rate of change of a function over time. Mathematically, it is the derivative of a function with respect to time. This concept can be likened to tracking...
164
Inverse z-Transform by Partial Fraction Expansion
263
The inverse z-transform is a crucial technique for converting a function from its z-domain representation back to the time domain. One effective method for finding the inverse z-transform is the Partial Fraction Method, which involves decomposing a function into simpler fractions with distinct coefficients. These fractions correspond to known z-transform pairs, facilitating the inverse transformation process.
To begin the process, the poles of the function are identified and the function is...
To begin the process, the poles of the function are identified and the function is...
263
Properties of Fourier Transform I
152
The application of Fourier Transform properties in radio broadcasting is multifaceted, enabling significant advancements in the way signals are transmitted and received. Key areas where these properties are utilized include simultaneous multi-channel transmission, audio clip speed adjustments, live broadcast delays for different time zones, audio frequency adjustments, and signal demodulation.
In radio broadcasting, multiple audio signals often need to be transmitted simultaneously. The Fourier...
In radio broadcasting, multiple audio signals often need to be transmitted simultaneously. The Fourier...
152
Trigonometric Fourier series
173
Fourier series is a foundational mathematical technique that decomposes periodic functions into an infinite series of sinusoidal harmonics. This method enables the representation of complex periodic signals as sums of simple sine and cosine functions, facilitating their analysis and interpretation in various fields, including signal processing, acoustics, and electrical engineering.
The trigonometric Fourier series specifically expresses a periodic function with a defined period T using sine...
The trigonometric Fourier series specifically expresses a periodic function with a defined period T using sine...
173


