Results 61 to 70 of about 20,315 (242)

Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition

Mathematics, 2020
This paper presents a class of implicit pantograph fractional differential equation with more general Riemann-Liouville fractional integral condition. A certain class of generalized fractional derivative is used to set the problem.
Idris Ahmed, Poom Kumam, K. Shah, Piyachat Borisut, K. Sitthithakerngkiet, Musa A. Demba   +5 more
semanticscholar   +1 more source

Fourth-order effective approximation of the normalized Riemann-Liouville tempered fractional derivatives and its applications

AIMS Mathematics
In this paper, a fourth-order quasi-compact approximation for the normalized Riemann-Liouville tempered fractional derivatives was proposed. Its effectiveness was proved by using the generating function method, and it was applied to the numerical ...
Jianxin Li, Zeshan Qiu
doaj   +1 more source

Existence of Solutions for Riemann-Liouville Fractional Boundary Value Problem

Abstract and Applied Analysis, 2014
By using the method of upper and lower solutions and fixed point theorems, the existence of solutions for a Riemann-Liouville fractional boundary value problem with the nonlinear term depending on fractional derivative of lower order is obtained under ...
Wenzhe Xie, Jing Xiao, Zhiguo Luo
doaj   +1 more source

Lie symmetry analysis, conservation laws and exact solutions of the seventh-order time fractional Sawada–Kotera–Ito equation

Results in Physics, 2016
In this paper Lie symmetry analysis of the seventh-order time fractional Sawada–Kotera–Ito (FSKI) equation with Riemann–Liouville derivative is performed.
Emrullah Yaşar, Yakup Yıldırım, Chaudry Masood Khalique   +2 more
doaj   +1 more source

Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative [PDF]

, 2007
2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05The Caputo fractional derivative is one of the most used definitions of a fractional derivative along with the Riemann-Liouville and the Grünwald- Letnikov ones.
Luchko, Yury, Trujillo, Juan
core  

On the Leibniz rule and Laplace transform for fractional derivatives

, 2019
Taylor series is a useful mathematical tool when describing and constructing a function. With the series representation, some properties of fractional calculus can be revealed clearly.
Liu, Da-Yan, Tse, Peter W., Wang, Yong, Wei, Yiheng   +3 more
core   +3 more sources

Ground state solutions of p-Laplacian singular Kirchhoff problem involving a Riemann-Liouville fractional derivative

Filomat, 2019
The purpose of this paper is to study the existence and multiplicity of solutions to the following Kirchhoff equation with singular nonlinearity and Riemann-Liouville Fractional Derivative: (P?){a+b ?T0|0D?t(u(t))|pdt)p-1 tD?T (?p(0D?tu(t)) = ?g(t)/u ...
M. Kratou
semanticscholar   +1 more source

A highly accurate numerical method for solving boundary value problem of generalized Bagley‐Torvik equation

Mathematical Methods in the Applied Sciences, EarlyView.
A highly accurate numerical method is given for the solution of boundary value problem of generalized Bagley‐Torvik (BgT) equation with Caputo derivative of order 0<β<2$$ 0<\beta <2 $$ by using the collocation‐shooting method (C‐SM). The collocation solution is constructed in the space Sm+1(1)$$ {S}_{m+1}^{(1)} $$ as piecewise polynomials of degree at ...
Suzan Cival Buranay, Mtema James Chin, Nazim I. Mahmudov   +2 more
wiley   +1 more source

A Simple and Effective Second-Order Numerical Algorithm for Tempered Fractional Differential Equation With Time Caputo-Tempered Fractional Derivative

Advances in Mathematical Physics
This paper presents an efficient numerical scheme for the space–time tempered fractional convection–diffusion equation, where the time derivative is the Caputo-tempered fractional derivative and the space derivatives are the normalized left and right ...
Dechao Gao, Zeshan Qiu, Lizan Wang, Jianxin Li   +3 more
doaj   +1 more source

Optimal error estimate of the Legendre spectral approximation for space-fractional reaction–advection–diffusion equation

Advances in Difference Equations, 2018
In this paper, we consider the space-fractional reaction–advection–diffusion equation with fractional diffusion and integer advection terms. By treating the first-order integer derivative as the composition of two Riemann–Liouville fractional derivative ...
Wenping Chen, Shujuan Lü, Hu Chen, Haiyu Liu   +3 more
doaj   +1 more source