Trends, directions for further research, and some open problems of fractional calculus
The area of fractional calculus (FC) has been fast develo** and is presently being applied
in all scientific fields. Therefore, it is of key relevance to assess the present state of …
in all scientific fields. Therefore, it is of key relevance to assess the present state of …
Review of some promising fractional physical models
VE Tarasov - International Journal of Modern Physics B, 2013 - World Scientific
Fractional dynamics is a field of study in physics and mechanics investigating the behavior
of objects and systems that are characterized by power-law nonlocality, power-law long-term …
of objects and systems that are characterized by power-law nonlocality, power-law long-term …
Investigating symmetric soliton solutions for the fractional coupled konno–onno system using improved versions of a novel analytical technique
The present research investigates symmetric soliton solutions for the Fractional Coupled
Konno–Onno System (FCKOS) by using two improved versions of an Extended Direct …
Konno–Onno System (FCKOS) by using two improved versions of an Extended Direct …
[LIVRE][B] Fractional order systems: modeling and control applications
This book aims to propose the implementation and application of Fractional Order Systems
(FOS). It is well known that FOS can be utilized in control applications and systems …
(FOS). It is well known that FOS can be utilized in control applications and systems …
[LIVRE][B] The fractional laplacian
This is a unique book that provides a comprehensive understanding of nonlinear equations
involving the fractional Laplacian as well as other nonlocal operators. Beginning from the …
involving the fractional Laplacian as well as other nonlocal operators. Beginning from the …
Fractional vector calculus and fractional Maxwell's equations
VE Tarasov - Annals of Physics, 2008 - Elsevier
The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville,
Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only …
Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only …
Discovering novel soliton solutions for (3+ 1)-modified fractional Zakharov–Kuznetsov equation in electrical engineering through an analytical approach
In recent years, the modified Extended Direct Algebraic Method (mEDAM) has demonstrated
to be an effective method for finding novel soliton solutions to nonlinear Fractional Partial …
to be an effective method for finding novel soliton solutions to nonlinear Fractional Partial …
On the continuum limit for discrete NLS with long-range lattice interactions
We consider a general class of discrete nonlinear Schrödinger equations (DNLS) on the
lattice h Z with mesh size h> 0. In the continuum limit when h→ 0, we prove that the limiting …
lattice h Z with mesh size h> 0. In the continuum limit when h→ 0, we prove that the limiting …
[HTML][HTML] Liouville theorems involving the fractional Laplacian on a half space
Let R+ n be the upper half Euclidean space and let α be any real number between 0 and 2.
Consider the following Dirichlet problem involving the fractional Laplacian:(1){(− Δ) α/2 u …
Consider the following Dirichlet problem involving the fractional Laplacian:(1){(− Δ) α/2 u …
Sufficient and necessary conditions for the fractional Gagliardo-Nirenberg inequalities and applications to Navier-Stokes and generalized Boson equations
H Hajaiej, L Molinet, T Ozawa, B Wang - arxiv preprint arxiv:1004.4287, 2010 - arxiv.org
Sufficient and necessary conditions for the generalized Gagliardo-Nirenberg (GN) inequality
in Besov spaces and Triebel-Lizorkin spaces are obtained. Applying the GN inequality, we …
in Besov spaces and Triebel-Lizorkin spaces are obtained. Applying the GN inequality, we …