A practical guide to Prabhakar fractional calculus
Abstract The Mittag–Leffler function is universally acclaimed as the Queen function of
fractional calculus. The aim of this work is to survey the key results and applications …
fractional calculus. The aim of this work is to survey the key results and applications …
Applications of distributed-order fractional operators: A review
Distributed-order fractional calculus (DOFC) is a rapidly emerging branch of the broader
area of fractional calculus that has important and far-reaching applications for the modeling …
area of fractional calculus that has important and far-reaching applications for the modeling …
Stability of a nonlinear Langevin system of ML-type fractional derivative affected by time-varying delays and differential feedback control
K Zhao - Fractal and Fractional, 2022 - mdpi.com
The Langevin system is an important mathematical model to describe Brownian motion. The
research shows that fractional differential equations have more advantages in …
research shows that fractional differential equations have more advantages in …
Existence and UH-stability of integral boundary problem for a class of nonlinear higher-order Hadamard fractional Langevin equation via Mittag-Leffler functions
K Zhao - Filomat, 2023 - doiserbia.nb.rs
The Langevin equation is a very important mathematical model in describing the random
motion of particles. The fractional Langevin equation is a powerful tool in complex …
motion of particles. The fractional Langevin equation is a powerful tool in complex …
Collocation methods for fractional differential equations involving non-singular kernel
A system of fractional differential equations involving non-singular Mittag-Leffler kernel is
considered. This system is transformed to a type of weakly singular integral equations in …
considered. This system is transformed to a type of weakly singular integral equations in …
Stability of a nonlinear fractional Langevin system with nonsingular exponential kernel and delay control
K Zhao - Discrete Dynamics in Nature and Society, 2022 - Wiley Online Library
Fractional Langevin system has great advantages in describing the random motion of
Brownian particles in complex viscous fluid. This manuscript deals with a delayed nonlinear …
Brownian particles in complex viscous fluid. This manuscript deals with a delayed nonlinear …
From continuous time random walks to the generalized diffusion equation
We obtain a generalized diffusion equation in modified or Riemann-Liouville form from
continuous time random walk theory. The waiting time probability density function and mean …
continuous time random walk theory. The waiting time probability density function and mean …
On fractional Langevin equation involving two fractional orders
O Baghani - Communications in Nonlinear Science and Numerical …, 2017 - Elsevier
In numerical analysis, it is frequently needed to examine how far a numerical solution is from
the exact one. To investigate this issue quantitatively, we need a tool to measure the …
the exact one. To investigate this issue quantitatively, we need a tool to measure the …
Distributed-order diffusion equations and multifractality: Models and solutions
We study distributed-order time fractional diffusion equations characterized by multifractal
memory kernels, in contrast to the simple power-law kernel of common time fractional …
memory kernels, in contrast to the simple power-law kernel of common time fractional …
Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel
We consider anomalous stochastic processes based on the renewal continuous time
random walk model with different forms for the probability density of waiting times between …
random walk model with different forms for the probability density of waiting times between …