Results 51 to 60 of about 21,294 (235)

Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by BPs Operational Matrices

Advances in Mathematical Physics, 2013
We present two methods for solving a nonlinear system of fractional differential equations within Caputo derivative. Firstly, we derive operational matrices for Caputo fractional derivative and for Riemann-Liouville fractional integral by using the ...
Mohsen Alipour, Dumitru Baleanu
doaj   +1 more source

Mathematical Model of Fractional Duffing Oscillator with Variable Memory

Mathematics, 2020
The article investigates a mathematical model of the Duffing oscillator with a variable fractional order derivative of the Riemann–Liouville type. The study of the model is carried out using a numerical scheme based on the approximation of the fractional
Valentine Kim, Roman Parovik
doaj   +1 more source

The Approximate Analytic Solution of the Time-Fractional Black-Scholes Equation with a European Option Based on the Katugampola Fractional Derivative

Mathematics, 2021
In the finance market, it is well known that the price change of the underlying fractal transmission system can be modeled with the Black-Scholes equation.
Sivaporn Ampun, Panumart Sawangtong
doaj   +1 more source

Fractional generalizations of filtering problems and their associated fractional Zakai equations [PDF]

, 2014
In this paper we discuss fractional generalizations of the filtering problem. The ”fractional” nature comes from time-changed state or observation processes, basic ingredients of the filtering problem. The mathematical feature of the fractional filtering
Daum, Frederick, Nelson, Kenric, Umarov, Sabir   +2 more
core   +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

Space-Time Fractional Reaction-Diffusion Equations Associated with a Generalized Riemann-Liouville Fractional Derivative [PDF]

Axioms, 2014
This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized Riemann-
R. Saxena, A. Mathai, H. Haubold
semanticscholar   +1 more source

Generalized Tu Formula and Hamilton Structures of Fractional Soliton Equation Hierarchy

, 2010
With the modified Riemann-Liouville fractional derivative, a fractional Tu formula is presented to investigate generalized Hamilton structure of fractional soliton equations.
Adda, Adda, Adda, Agrawal, Agrawal, Almeida, Baleanu, Baleanu, Carpinter, Carpinteri, Carpinteri, Carpinteri, Chen, Chen, Chen, Chen, Cottrill-Shepherd, Cottrill-Shepherd, Cresson, Cresson, El Naschie, El Naschie, El-Nabulsi, El-Nabulsi, El-Nabulsi, Frederico, Fujioka, Fujioka, Guo, Guo-cheng Wu, Jumarie, Jumarie, Jumarie, Jumarie, Kazbekov, Kilbas, Kiryakova, Kolwankar, Kolwankar, Kolwankar, Lakshmikantham, Liang, Ma, Ma, Ma, Malinowska, Miller, Nicholas, Nottale, Nottale, Parvate, Podlubny, Purkait, Riewe, Riewe, Sheng Zhang, Tarasov, Tarasov, Tu, West, Wu, Wu, Wu, Wu, Xia   +64 more
core   +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

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