Related Experiment Video
Updated: May 24, 2025

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
Published on: August 30, 2013
On generalized fractal-fractional derivative and integral operators associated with generalized Mittag-Leffler
Hira Khan1, Gauhar Rahman1, Muhammad Samraiz2
1Department of Mathematics and Statistics, Hazara University, Mansehra, 21300, Pakistan.
Abstract:
In recent years, the Atangana-Baleanu (AB) fractal-fractional derivatives are widely used in many fields. In 2017, Atangana defined such operators by utilizing one parameter Mittag-Leffler function (M-L) function. Such operators have not yet been studied for three parameters M-L function. In this paper, we discuss further modifications of Caputo Fabrizio (CF), AB and generalized Hattaf fractal-fractional (GHF) operators. We used the modified three parameters M-L function to define the generalized fractal-fractional (GFF) differential and integral operators. We study an innovative class of new generalized weighted differential and integral operators. We define the generalized fractal-fractional (GFF) differential and integral operators with generalized Mittag-Leffler (M-L) kernels, which are used to simulate the complex dynamics of several natural and physical phenomena in a variety of scientific and engineering domains. There are a few established features of the newly defined operators. An example of an application for this new class of GFF integral is presented. Also, we discussed the graphical comparison of this new GFF operator with the existing GHF, AB and CF derivatives. Our case is the more general case compared with the existing fractal-fractional operators. We have presented some novel results for the new operators both analytically and graphically. Also, we discussed some special cases by giving specific value to the parameter . All the classical operators are restored by applying certain conditions on parameters.
Related Concept Videos
Second Derivatives and Laplace Operator
Consider a scalar function. The curl of its...
Gradient and Del Operator
Properties of Laplace Transform-II
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...
Inverse z-Transform by Partial Fraction Expansion
To begin the process, the poles of the function are identified and the function is...
Properties of Fourier Transform I
In radio broadcasting, multiple audio signals often need to be transmitted simultaneously. The Fourier...
Trigonometric Fourier series
The trigonometric Fourier series specifically expresses a periodic function with a defined period T using sine...

