Results 51 to 60 of about 12,553 (141)

Solutions to Riemann–Liouville fractional integrodifferential equations via fractional resolvents

Advances in Difference Equations, 2019
This paper is concerned with the semilinear fractional integrodifferential system with Riemann–Liouville fractional derivative. Firstly, we introduce the suitable C1−α $C_{1-\alpha }$-solution to Riemann–Liouville fractional integrodifferential equations
Shaochun Ji, Dandan Yang
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A Finite Element Method for the Fractional Sturm-Liouville Problem [PDF]

, 2013
In this work, we propose an efficient finite element method for solving fractional Sturm-Liouville problems involving either the Caputo or Riemann-Liouville derivative of order $\alpha\in(1,2)$ on the unit interval $(0,1)$.
Jin, Bangti, Lazarov, Raytcho, Pasciak, Joseph, Rundell, William   +3 more
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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
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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
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Improvement on Conformable Fractional Derivative and Its Applications in Fractional Differential Equations

Journal of Function Spaces, 2020
In this paper, we made improvement on the conformable fractional derivative. Compared to the original one, the improved conformable fractional derivative can be a better replacement of the classical Riemann-Liouville and Caputo fractional derivative in ...
Feng Gao, Chunmei Chi
doaj   +1 more source

Hilfer-Prabhakar Derivatives and Some Applications

, 2014
We present a generalization of Hilfer derivatives in which Riemann--Liouville integrals are replaced by more general Prabhakar integrals. We analyze and discuss its properties.
Garra, Roberto, Gorenflo, Rudolf, Polito, Federico, Tomovski, Zivorad   +3 more
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Oscillation of solutions to nonlinear forced fractional differential equations

Electronic Journal of Differential Equations, 2013
In this article, we study the oscillation of solutions to a nonlinear forced fractional differential equation. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative.
Qinghua Feng, Fanwei Meng
doaj  

Fractional-order boundary value problem with Sturm-Liouville boundary conditions

Electronic Journal of Differential Equations, 2015
Using the new conformable fractional derivative, which differs from the Riemann-Liouville and Caputo fractional derivatives, we reformulate the second-order conjugate boundary value problem in this new setting.
Douglas R. Anderson, Richard I. Avery
doaj  

Extending the D'Alembert Solution to Space-Time Modified Riemann-Liouville Fractional Wave Equations

, 2012
In the realm of complexity, it is argued that adequate modeling of TeV-physics demands an approach based on fractal operators and fractional calculus (FC). Non-local theories and memory effects are connected to complexity and the FC.
-Sheng Duan, Baleanu, Bollini, Calcagni, Cresus F.L. Godinho, Fadeev, Goldfain, Guelfand, Herrmann, Hohenberg, Horava, Hornreich, J. Weberszpil, J.A. Helayël-Neto, Jumarie, Jumarie, Lifshitz, Ma, Metzler, Miller, Nobre, Nottale, Nottale, Plyushchay, Raspini, Weinberg   +25 more
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Fractional isoperimetric Noether's theorem in the Riemann-Liouville sense

, 2013
We prove Noether-type theorems for fractional isoperimetric variational problems with Riemann-Liouville derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples, in the fractional context of the calculus of variations,
Almeida, Almeida, Atanacković, Atanacković, Baleanu, Bartosiewicz, Chen, Delfim F.M. Torres, El-Nabulsi, Ferreira, Frederico, Frederico, Frederico, Frederico, Gastão S.F. Frederico, Gelfand, Herzallah, Hilfer, Jafari, Kilbas, Kiryakova, Kiryakova, Klimek, Leitmann, Malinowska, Malinowska, Malinowska, Martins, Odzijewicz, Odzijewicz, Podlubny, Pooseh, Pooseh, Riewe, Riewe, Torres, Torres, Torres, Torres, van Brunt   +39 more
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