A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications
Variable-order (VO) fractional differential equations (FDEs) with a time (t), space (x) or other
variables dependent order have been successfully applied to investigate time and/or space …
variables dependent order have been successfully applied to investigate time and/or space …
Applications of variable-order fractional operators: a review
S Patnaik, JP Hollkamp… - Proceedings of the …, 2020 - royalsocietypublishing.org
Variable-order fractional operators were conceived and mathematically formalized only in
recent years. The possibility of formulating evolutionary governing equations has led to the …
recent years. The possibility of formulating evolutionary governing equations has led to the …
[BOOK][B] Numerical methods for fractional calculus
This book provides efficient and reliable numerical methods for solving fractional calculus
problems. It focuses on numerical techniques for fractional integrals, derivatives, and …
problems. It focuses on numerical techniques for fractional integrals, derivatives, and …
New variable-order fractional chaotic systems for fast image encryption
New variable-order fractional chaotic systems are proposed in this paper. A concept of short
memory is introduced where the initial point in the Caputo derivative is varied. The fractional …
memory is introduced where the initial point in the Caputo derivative is varied. The fractional …
[BOOK][B] General fractional derivatives with applications in viscoelasticity
General Fractional Derivatives with Applications in Viscoelasticity introduces the newly
established fractional-order calculus operators involving singular and non-singular kernels …
established fractional-order calculus operators involving singular and non-singular kernels …
Advanced materials modelling via fractional calculus: challenges and perspectives
G Failla, M Zingales - Philosophical Transactions of the …, 2020 - royalsocietypublishing.org
Fractional calculus is now a well-established tool in engineering science, with very
promising applications in materials modelling. Indeed, several studies have shown that …
promising applications in materials modelling. Indeed, several studies have shown that …
Short memory fractional differential equations for new memristor and neural network design
Fractional derivatives hold memory effects, and they are extensively used in various real-
world applications. However, they also need large storage space and cause poor efficiency …
world applications. However, they also need large storage space and cause poor efficiency …
A novel fractional order fuzzy PID controller and its optimal time domain tuning based on integral performance indices
A novel fractional order (FO) fuzzy Proportional-Integral-Derivative (PID) controller has been
proposed in this paper which works on the closed loop error and its fractional derivative as …
proposed in this paper which works on the closed loop error and its fractional derivative as …
Second-order approximations for variable order fractional derivatives: algorithms and applications
Fractional calculus allows variable-order of fractional operators, which can be exploited in
diverse physical and biological applications where rates of change of the quantity of interest …
diverse physical and biological applications where rates of change of the quantity of interest …
Finite difference methods for fractional differential equations
In this review paper, the finite difference methods (FDMs) for the fractional differential
equations are displayed. The considered equations mainly include the fractional kinetic …
equations are displayed. The considered equations mainly include the fractional kinetic …