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Jacobi–Gauss–Lobatto collocation approach for non-singular variable-order time fractional generalized Kuramoto–Sivashinsky equation
This paper introduces the non-singular variable-order (VO) time fractional version of the generalized Kuramoto–Sivashinsky (GKS) equation with the...
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Simulation of 2D and 3D inverse source problems of nonlinear time-fractional wave equation by the meshless homogenization function method
In this paper, homogenization functions are first proposed to address two-dimensional (2D) and three-dimensional (3D) inverse source problems of...
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A boundary element method formulation based on the Caputo derivative for the solution of the diffusion-wave equation
A boundary element method formulation is developed and validated through the solution of problems governed by the diffusion-wave equation, for which...
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Edge detection using the Prewitt operator with fractional order telegraph partial differential equations (PreFOTPDE)
Detecting edges in image processing is an important process in image analysis or enhancement. Many methods detected edge information based on the...
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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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A novel alternating-direction implicit spectral Galerkin method for a multi-term time-space fractional diffusion equation in three dimensions
In this paper, we develop an efficient spectral Galerkin method for the three-dimensional (3D) multi-term time-space fractional diffusion equation....
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Magneto-thermoelastic behaviour of a finite viscoelastic rotating rod by incorporating Eringen’s theory and heat equation including Caputo–Fabrizio fractional derivative
This paper addresses a modified constitutive equation by incorporating the size effect of nanostructured materials and a new formulation of Fourier's...
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Fitted schemes for Caputo-Hadamard fractional differential equations
In the present paper, the regularity and finite difference methods for Caputo-Hadamard fractional differential equations with initial value...
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Exponential synchronization of fractional-order multilayer coupled neural networks with reaction-diffusion terms via intermittent control
In this paper, the issue of exponential synchronization of fractional-order multilayer coupled neural networks with reaction-diffusion terms is...
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A computational approach for the space-time fractional advection–diffusion equation arising in contaminant transport through porous media
The fractional advection–diffusion equation, known as non-local diffusion, is a relationship utilized in groundwater hydrology as a reliable means of...
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An efficient optimization algorithm for nonlinear 2D fractional optimal control problems
In this research article, we present an optimization algorithm aimed at finding the optimal solution for nonlinear 2-dimensional fractional optimal...
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Chaotic synchronization and fractal interpolation-based image encryption: exploring event-triggered impulsive control in variable-order fractional lur’e systems
This paper investigates the event-triggered impulsive synchronization of a variable-order fractional chaotic Lur’e system with the application of...
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Solving a generalized order improved diffusion equation of image denoising using a CeNN-based scheme
This paper presents a novel algorithm for image denoising using an improved nonlinear diffusion PDE model and a cellular neural network (CeNN)...
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Complex Turing patterns in chaotic dynamics of autocatalytic reactions with the Caputo fractional derivative
Many chemical systems exhibit a range of patterns, a noticeable and interesting class of numerical patterns that arise in autocatalytic reactions...
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Unconditional energy stability and maximum principle preserving scheme for the Allen-Cahn equation
In this paper, we propose a novel fully implicit numerical scheme that satisfies both nonlinear energy stability and maximum principle for the space...
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A fast linearized numerical method for nonlinear time-fractional diffusion equations
In this paper, we study a fast linearized numerical method for solving nonlinear time-fractional diffusion equations. A new weighted method is...
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Fractional-order Chelyshkov wavelet method for solving variable-order fractional differential equations and an application in variable-order fractional relaxation system
We give an efficient numerical approach to solve variable-order fractional differential equations (VO-FDEs) by applying fractional-order generalized...
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A local meshless method for time fractional nonlinear diffusion wave equation
We present a radial basis function-based local collocation method for solving time fractional nonlinear diffusion wave equation.The main beauty of...
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A survey of fractional calculus applications in artificial neural networks
Artificial neural network (ANN) is the backbone of machine learning, specifically deep learning. The interpolating and learning ability of an ANN...
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A Fractional Brownian Motion Approach to Psychological and Team Diffusion Problems
In this chapter we discuss drift diffusion and extensions to fractional Brownian motion. We include some Artificial Intelligence (AI) motivated...