Results 51 to 60 of about 2,558 (225)

Fractional derivative generalization of Noether’s theorem

Open Mathematics, 2015
The symmetry of the Bagley–Torvik equation is investigated by using the Lie group analysis method. The Bagley–Torvik equation in the sense of the Riemann–Liouville derivatives is considered.
Khorshidi Maryam, Nadjafikhah Mehdi, Jafari Hossein   +2 more
doaj   +1 more source

On the Hermite–Hadamard type inequality for ψ-Riemann–Liouville fractional integrals via convex functions

Journal of Inequalities and Applications, 2019
In this paper, we establish a new Hermite–Hadamard inequality involving left-sided and right-sided ψ-Riemann–Liouville fractional integrals via convex functions.
Kui Liu, JinRong Wang, Donal O’Regan
doaj   +1 more source

Finite Biorthogonal Polynomials Suggested by the Finite Orthogonal Polynomials Mnp,qx$$ {M}_n^{\left(p,q\right)}(x) $$

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Constructing a biorthogonal structure from scratch, that is, defining a biorthogonal pair is quite tough. Because here the orthogonality must be established between two different sets. There are four known univariate biorthogonal polynomial sets, suggested by Laguerre, Jacobi, Hermite and Szegő‐Hermite polynomials, in the literature.
Esra Güldoğan Lekesiz
wiley   +1 more source

Composition of Fractional Integral and Derivative Operators: Summarised in Tables

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT This paper compiles a complete, detailed list of composition properties for Riemann–Liouville fractional differintegrals, in all possible cases for orders anywhere in the complex plane, with the results presented clearly in a table for easy visual consumption.
Arran Fernandez
wiley   +1 more source

Survey and new results on boundary-value problems of singular fractional differential equations with impulse effects

Electronic Journal of Differential Equations, 2016
Firstly we prove existence and uniqueness of solutions of Cauchy problems of linear fractional differential equations (LFDEs) with two variable coefficients involving Caputo fractional derivative, Riemann-Liouville derivative, Caputo type Hadamard ...
Yuji Liu
doaj  

Numerical Discretization of Riemann–Liouville Fractional Derivatives with Strictly Positive Eigenvalues

AppliedMath
This paper investigates a unique and stable numerical approximation of the Riemann–Liouville Fractional Derivative. We utilize diagonal norm finite difference-based time integration methods within the summation-by-parts framework.
Sam Motsoka Rametse, Rhameez Sheldon Herbst   +1 more
doaj   +1 more source

A New Gronwall–Bellman Inequality in Frame of Generalized Proportional Fractional Derivative

Mathematics, 2019
New versions of a Gronwall−Bellman inequality in the frame of the generalized (Riemann−Liouville and Caputo) proportional fractional derivative are provided.
Jehad Alzabut, Weerawat Sudsutad, Zeynep Kayar, Hamid Baghani   +3 more
doaj   +1 more source

p-Moment Mittag–Leffler Stability of Riemann–Liouville Fractional Differential Equations with Random Impulses

Mathematics, 2020
Fractional differential equations with impulses arise in modeling real world phenomena where the state changes instantaneously at some moments. Often, these instantaneous changes occur at random moments.
Ravi Agarwal, Snezhana Hristova, Donal O’Regan, Peter Kopanov   +3 more
doaj   +1 more source

Fractional Moment Theory for Anomalous Transport: A Unified Framework for Lévy Flights, Fractals, and Complex Dynamical Systems

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT We develop a unified mathematical framework extending classical moment theory from discrete integer orders to a continuous spectrum of real orders f>0$$ f>0 $$, providing a systematic statistical characterization of complex systems exhibiting power‐law behavior.
Farrukh A. Chishtie
wiley   +1 more source

Ultrafast Diffusion Modeling via the Riemann–Liouville Nonlocal Structural Derivative and Its Application in Porous Media

Fractal and Fractional
Ultrafast diffusion disperses faster than super-diffusion, and this has been proven by several theoretical and experimental investigations. The mean square displacement of ultrafast diffusion grows exponentially, which provides a significant challenge ...
Wei Xu, Hui Liu, Lijuan Chen, Yongtao Zhou   +3 more
doaj   +1 more source