Study of multiple lump and rogue waves to the generalized unstable space time fractional nonlinear Schrödinger equation

STR Rizvi, AR Seadawy, S Ahmed, M Younis… - Chaos, Solitons & …, 2021 - Elsevier
This article possess lump, lump with one kink, lump with two kink, rogue wave and lump
interactions with periodic and kink solitons for the generalized unstable space time fractional …

Modeling attractors of chaotic dynamical systems with fractal–fractional operators

A Atangana, S Qureshi - Chaos, solitons & fractals, 2019 - Elsevier
In this paper, newly proposed differential and integral operators called the fractal–fractional
derivatives and integrals have been used to predict chaotic behavior of some attractors from …

Fractal-fractional differentiation and integration: connecting fractal calculus and fractional calculus to predict complex system

A Atangana - Chaos, solitons & fractals, 2017 - Elsevier
New operators of differentiation have been introduced in this paper as convolution of power
law, exponential decay law, and generalized Mittag-Leffler law with fractal derivative. The …

An overview of mathematical modelling in cancer research: fractional calculus as modelling tool

LC Vieira, RS Costa, D Valério - Fractal and Fractional, 2023 - mdpi.com
Cancer is a complex disease, responsible for a significant portion of global deaths. The
increasing prioritisation of know-why over know-how approaches in biological research has …

A survey of models of ultraslow diffusion in heterogeneous materials

Y Liang, S Wang, W Chen… - Applied …, 2019 - asmedigitalcollection.asme.org
Ultraslow diffusion is characterized by a logarithmic growth of the mean squared
displacement (MSD) as a function of time. It occurs in complex arrangements of molecules …

[BUKU][B] Theory and numerical approximations of fractional integrals and derivatives

C Li, M Cai - 2019 - SIAM
Fractional calculus, which has two main features—singularity and nonlocality from its origin—
means integration and differentiation of any positive real order or even complex order. It has …

Applications of fractional calculus in computer vision: a survey

S Arora, T Mathur, S Agarwal, K Tiwari, P Gupta - Neurocomputing, 2022 - Elsevier
Fractional calculus is an abstract idea exploring interpretations of differentiation having non-
integer order. For a very long time, it was considered as a topic of mere theoretical interest …

Mathematical model of survival of fractional calculus, critics and their impact: How singular is our world?

A Atangana - Advances in Difference Equations, 2021 - Springer
Fractional calculus as was predicted by Leibniz to be a paradox, has nowadays evolved to
become a centre of interest for many researchers from various backgrounds. As a result …

[PDF][PDF] Advanced local fractional calculus and its applications

XJ Yang - 2012 - researchgate.net
This monograph is an invitation both to the interested scientists and the engineers. It
presents a thorough introduction to the recent results of local fractional calculus. It is also …

[BUKU][B] Fractional calculus and waves in linear viscoelasticity: an introduction to mathematical models

F Mainardi - 2022 - books.google.com
Fractional Calculus and Waves in Linear Viscoelasticity (Second Edition) is a self-contained
treatment of the mathematical theory of linear (uni-axial) viscoelasticity (constitutive equation …