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Dynamic analysis on Liu system under fractal–fractional differentiation
The exploration of fractal geometry and fractional calculus aids in comprehending intricate dynamic behavior, thereby enhancing our understanding of...
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Effect of a new local derivative on space-time fractional nonlinear Schrödinger equation and its stability analysis
The study presented investigates the space-time fractional nonlinear Schrödinger equation, which is important in telecommunication industry,...
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New semi-analytical solution of fractional Newell–Whitehead–Segel equation arising in nonlinear optics with non-singular and non-local kernel derivative
In this paper, a combined form of Laplace transform is applied with the Adomian Decomposition technique for the first time to obtain new...
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Application of efficient hybrid local meshless method for the numerical simulation of time-fractional PDEs arising in mathematical physics and finance
The article describes the implementation of an efficient hybrid local meshless technique for the numerical solution of a multi-term time-fractional...
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Two-weight Norm Inequalities for Local Fractional Integrals on Gaussian Measure Spaces
In this paper, the authors establish the two-weight boundedness of the local fractional maximal operators and local fractional integrals on Gaussian...
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Fractal and Fractional Calculus
It has been 2000 years since the third century BC, when Euclidean geometry was established by Euclid. This system has been considered as a definite,...
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Fractional Bessel Derivative Within the Mellin Transform Framework
In this paper, we present a fresh perspective on the fractional power of the Bessel operator using the Mellin transform. Drawing inspiration from the...
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Mathematical model of survival of fractional calculus, critics and their impact: How singular is our world?
Fractional calculus as was predicted by Leibniz to be a paradox, has nowadays evolved to become a centre of interest for many researchers from...
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Mixed sequential type pantograph fractional integro-differential equations with non-local boundary conditions
In this paper, we investigate the existence, uniqueness and stability of solutions to the mixed sequential pantograph fractional integro-differential...
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Fractional Spectral and Fractional Finite Element Methods: A Comprehensive Review and Future Prospects
In this article, we will discuss the applications of the Spectral element method (SEM) and Finite element Method (FEM) for fractional calculusThe...
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Fractional Derivative Models
Models that are described by the differential equations with the derivatives of the fractional order are considered including the fractional Fourier...
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Modeling the dynamics of tumor–immune cells interactions via fractional calculus
The immune response in the tumor micro-environment is a complicated biological phenomenon that needs to be investigated further. It is eminent that...
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Precise Local Estimates for Differential Equations driven by Fractional Brownian Motion: Elliptic Case
This article is concerned with stochastic differential equations driven by a d -dimensional fractional Brownian motion with Hurst parameter
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Medical image segmentation model based on caputo fractional differential
Medical image segmentation technology, as a key work of modern medical such as intelligent medical diagnosis, has attracted a lot of attention....
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Why Do Big Data and Machine Learning Entail the Fractional Dynamics?
Chapter 2 explores the fundamental question of why big data and machine learning inherently involve...
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An Adaptive Learning Rate Deep Learning Optimizer Using Long and Short-Term Gradients Based on G–L Fractional-Order Derivative
Deep learning model is a multi-layered network structure, and the network parameters that evaluate the final performance of the model must be trained...
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Axi-Symmetric Problem in the Thermoelastic Medium under Moore-Gibson-Thompson Heat Equation with Hyperbolic Two Temperature, Non-Local and Fractional Order
AbstractIn this manuscript, a two-dimensional axi-symmetric problem within a thermoelastic medium featuring fractional order derivatives, focusing on...
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General Fractional Calculus with Nonsingular Kernels: New Prospective on Viscoelasticity
In the chapter, the general fractional derivatives in the different kernel functions, such as Mittag-Lefller, Wiman and Prabhakar functions are...
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A Computational Study of Local Fractional Helmholtz and Coupled Helmholtz Equations in Fractal Media
In this manuscript, an approximate analytical solution of the Helmholtz and coupled Helmholtz equations of fractional order is obtained using local...