Decolonisation of fractional calculus rules: breaking commutativity and associativity to capture more natural phenomena
A Atangana, JF Gómez-Aguilar - The European Physical Journal Plus, 2018 - Springer
To answer some issues raised about the concept of fractional differentiation and integration
based on the exponential and Mittag-Leffler laws, we present, in this paper, fundamental …
based on the exponential and Mittag-Leffler laws, we present, in this paper, fundamental …
Non validity of index law in fractional calculus: a fractional differential operator with Markovian and non-Markovian properties
A Atangana - Physica A: statistical mechanics and its applications, 2018 - Elsevier
We presented an analysis of evolutions equations generated by three fractional derivatives
namely the Riemann–Liouville, Caputo–Fabrizio and the Atangana–Baleanu fractional …
namely the Riemann–Liouville, Caputo–Fabrizio and the Atangana–Baleanu fractional …
System of fractional differential algebraic equations with applications
One of the important classes of coupled systems of algebraic, differential and fractional
differential equations (CSADFDEs) is fractional differential algebraic equations (FDAEs) …
differential equations (CSADFDEs) is fractional differential algebraic equations (FDAEs) …
A Chebyshev spectral method based on operational matrix for fractional differential equations involving non-singular Mittag-Leffler kernel
In this paper, we solve a system of fractional differential equations within a fractional
derivative involving the Mittag-Leffler kernel by using the spectral methods. We apply the …
derivative involving the Mittag-Leffler kernel by using the spectral methods. We apply the …
New aspects of time fractional optimal control problems within operators with nonsingular kernel
This paper deals with a new formulation of time fractional optimal control problems governed
by Caputo-Fabrizio (CF) fractional derivative. The optimality system for this problem is …
by Caputo-Fabrizio (CF) fractional derivative. The optimality system for this problem is …
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 …
Fractional differential equation modeling of viscoelastic fluid in mass-spring-magnetorheological damper mechanical system
JE Escalante-Martínez, LJ Morales-Mendoza… - The European Physical …, 2020 - Springer
The mass-spring-damper system has the minimum complexity scenario which characterizes
almost all the mechanical vibration phenomena. Also it is well known that a second-order …
almost all the mechanical vibration phenomena. Also it is well known that a second-order …
[HTML][HTML] Embedding (3+ 1)-dimensional diffusion, telegraph, and Burgers' equations into fractal 2D and 3D spaces: an analytical study
Fractional derivatives can be utilized as a promising tool for characterizing systems with
embedded memory or describing viscoelasticity of advanced materials. Motivated by the …
embedded memory or describing viscoelasticity of advanced materials. Motivated by the …
Numerical Methods for Solving Systems of Atangana-Baleanu Fractional Differential Equations
This chapter reviews the recent developments of fractional calculus and the numerical
methods for fractional differential equations involving nonsingular Mittag-Leffler kernel. It …
methods for fractional differential equations involving nonsingular Mittag-Leffler kernel. It …
The non-uniqueness of solution for initial value problem of impulsive differential equations involving higher order Katugampola fractional derivative
XM Zhang - Advances in Difference Equations, 2020 - Springer
In this paper we consider the initial value problem for some impulsive differential equations
with higher order Katugampola fractional derivative (fractional order q∈(1, 2 q∈(1,2). The …
with higher order Katugampola fractional derivative (fractional order q∈(1, 2 q∈(1,2). The …