Applications of Distributed-Order Fractional Operators: A Review [PDF]
Entropy, 2021 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 of complex systems. DOFC generalizes the intrinsic multiscale nature of
Wei Ding +3 more
doaj +5 more sources
Stability Analysis of Distributed Order Fractional Chen System [PDF]
The Scientific World Journal, 2013 We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain.
H. Aminikhah +2 more
doaj +5 more sources
Pontryagin Maximum Principle for Distributed-Order Fractional Systems [PDF]
Mathematics, 2021 We consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove a strong necessary optimality condition of Pontryagin type.
Faïçal Ndaïrou, Delfim F. M. Torres
doaj +4 more sources
Stability Analysis of Distributed Order Fractional Differential Equations
Abstract and Applied Analysis, 2011 We analyze the stability of three classes of distributed order fractional differential equations (DOFDEs) with respect to the nonnegative density function.
H. Saberi Najafi +2 more
doaj +2 more sources
Multiscale nonlocal elasticity: A distributed order fractional formulation
International Journal of Mechanical Sciences, 2022 This study presents a generalized multiscale nonlocal elasticity theory that leverages distributed order fractional calculus to accurately capture coexisting multiscale and nonlocal effects within a macroscopic continuum. The nonlocal multiscale behavior is captured via distributed order fractional constitutive relations derived from a nonlocal ...
Wei Ding +2 more
exaly +3 more sources
Distributed order calculus and equations of ultraslow diffusion
Journal of Mathematical Analysis and Applications, 2008 39 pages. To appear in J. Math.
Anatoly N Kochubei
exaly +4 more sources
Numerical analysis for distributed-order differential equations
Journal of Computational and Applied Mathematics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kai Diethelm
exaly +3 more sources
A novel numerical approach for distributed order time fractional COVID-19 virus model [PDF]
Journal of Applied Research on Industrial Engineering, 2022 In this paper, we proposed a numerical approach to solve a distributed order time fractional COVID 19 virus model. The fractional derivatives are shown in the Caputo-Prabhakar contains generalized Mittag-Leffler Kernel.
Mohsen Khasteh +2 more
doaj +1 more source
A Matrix Transform Technique for Distributed-Order Time-Fractional Advection–Dispersion Problems
Fractal and Fractional, 2023 Invoking the matrix transfer technique, we propose a novel numerical scheme to solve the time-fractional advection–dispersion equation (ADE) with distributed-order Riesz-space fractional derivatives (FDs).
Mohammadhossein Derakhshan +4 more
doaj +1 more source
Stability Analysis of the Nabla Distributed-Order Nonlinear Systems
Fractal and Fractional, 2022 The stability of the nabla discrete distributed-order nonlinear dynamic systems is investigated in this paper. Firstly, a sufficient condition for the asymptotic stability of the nabla discrete distributed-order nonlinear systems is proposed based on ...
Cuihong Wang, Tianfen Zhu, Yangquan Chen
doaj +1 more source