Results 31 to 40 of about 19,827 (284)
Fractional Sobolev Spaces via Riemann-Liouville Derivatives [PDF]
Journal of Function Spaces and Applications, 2013 Using Riemann-Liouville derivatives, we introduce fractional Sobolev spaces, characterize them, define weak fractional derivatives, and show that they coincide with the Riemann-Liouville ones. Next, we prove equivalence of some norms in the introduced spaces and derive their completeness, reflexivity, separability, and compactness of some imbeddings ...
Dariusz Idczak, Stanisław Walczak
openaire +3 more sources
Mathematical Modelling and Analysis, 2017 This paper investigates fractional order Barbalat’s lemma and its applications for the stability of fractional order nonlinear systems with Caputo fractional derivative at first.
Fei Wang, Yongqing Yang
doaj +1 more source
Fractional boundary value problems with Riemann-Liouville fractional derivatives [PDF]
Advances in Difference Equations, 2015 In this paper, by employing two fixed point theorems of a sum operators, we investigate the existence and uniqueness of positive solutions for the following fractional boundary value problems: $-D_{0+}^{\alpha}x(t)=f(t, x(t),
Caozong Cheng, Jingjing Tan
openaire +2 more sources
A possible generalization of acoustic wave equation using the concept of perturbed derivative order [PDF]
, 2013 The standard version of acoustic wave equation is modified using the concept of the generalized Riemann-Liouville fractional order derivative. Some properties of the generalized Riemann-Liouville fractional derivative approximation are presented.
Atangana, Abdon, Kilicman, Adem
core +3 more sources
The unified Riemann-Liouville fractional derivative formulae
Tamkang Journal of Mathematics, 2005 In this paper, we obtain two unified fractional derivative formulae. The first involves the product of two general class of polynomials and the multivariable $H$-function. The second fractional derivative formula also involves the product of two general class of polynomials and the multivariable $H$-function and has been obtained by the application of ...
R. C. Soni, Deepika Singh
openaire +4 more sources
On a certain extension of the Riemann-Liouville fractional derivative operator [PDF]
arXiv: Classical Analysis and ODEs, 2018 15
Nisar Sooppy Kottakkaran Sooppy +3 more
openaire +2 more sources
On the solution of the space-time fractional cubic nonlinear Schrödinger equation
Results in Physics, 2018 The space–time fractional nonlinear Schrödinger equation is studied based on the modified Riemann–Liouville derivative. The fractional mapping expansion method is used to find analytical solution of this model.
E.A. Yousif +2 more
doaj +1 more source
Approximation with Riemann-Liouville fractional derivatives [PDF]
Studia Universitatis Babes-Bolyai Matematica, 2019 n this article we study quantitatively with rates the pointwise convergence of a sequence of positive sublinear operators to the unit operator over continuous functions. This takes place under low order smothness,less than one, of the approximated function and it is expressed via the left and right Riemann-Liouville fractional derivatives of it.
openaire +2 more sources
Analysis of fractional differential systems involving Riemann Liouville fractional derivative
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2020 This paper is devoted to studying the multiple positive solutions for a system of nonlinear fractional boundary value problems. Our analysis is based upon the Avery Peterson fixed point theorem. in addition, we include an example for the demonstration of our main result.
Batik, Songül, Deren, Fulya Yörük
openaire +7 more sources
Solution of Fractional Order Equations in the Domain of the Mellin Transform
Journal of Nigerian Society of Physical Sciences, 2019 This paper presents the Mellin transform for the solution of the fractional order equations. The Mellin transform approach occurs in many areas of applied mathematics and technology.
Sunday Emmanuel Fadugba
doaj +1 more source