Results 121 to 130 of about 56,900 (290)

Exponential Stability of Higher Order Fractional Neutral Stochastic Differential Equation Via Integral Contractors

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6425-6446, April 2025.
ABSTRACT The well‐posedness results for mild solutions to the fractional neutral stochastic differential system with Rosenblatt process with Hurst index Ĥ∈12,1$$ \hat{H}\in \left(\frac{1}{2},1\right) $$ is discussed in this article. To demonstrate the results, the concept of bounded integral contractors is combined with the stochastic result and ...
Dimplekumar N. Chalishajar, Dhanalakshmi Kasinathan, Ramkumar Kasinathan, Ravikumar Kasinathan   +3 more
wiley   +1 more source

Equivalences of Nonlinear Higher Order Fractional Differential Equations With Integral Equations

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6930-6942, April 2025.
ABSTRACT Equivalences of initial value problems (IVPs) of both nonlinear higher order (Riemann–Liouville type) fractional differential equations (FDEs) and Caputo FDEs with the corresponding integral equations are studied in this paper. It is proved that the nonlinearities in the FDEs can be L1$$ {L}^1 $$‐Carathéodory with suitable conditions.
Kunquan Lan
wiley   +1 more source

The dynamics of Zika virus with Caputo fractional derivative

AIMS Mathematics, 2019
In the present paper, we investigate a fractional model in Caputo sense to explore the dynamics of the Zika virus. The basic results of the fractional Zika model are presented.
Muhammad Altaf Khan, Saif Ullah, Muhammad Farhan   +2 more
semanticscholar   +1 more source

Generalized time fractional IHCP with Caputo fractional derivatives

Journal of Physics: Conference Series, 2008
The numerical solution of the generalized time fractional inverse heat conduction problem (GTFIHCP) on a finite slab is investigated in the presence of measured (noisy) data when the time fractional derivative is interpreted in the sense of Caputo. The GTFIHCP involves the simultaneous identification of the heat flux and temperature transient functions
Diego A. Murio, Carlos E. Mejía
openaire   +2 more sources

Generalized Hyers–Ulam Stability of Laplace Equation With Neumann Boundary Condition in the Upper Half‐Space

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT This paper investigates the generalized Hyers–Ulam stability of the Laplace equation subject to Neumann boundary conditions in the upper half‐space. Traditionally, Hyers–Ulam stability problems for differential equations are analyzed by examining the system's error, particularly in relation to a forcing term.
Dongseung Kang, Hoewoon B. Kim, Dojin Kim   +2 more
wiley   +1 more source

The Analytical Solution for the Black-Scholes Equation with Two Assets in the Liouville-Caputo Fractional Derivative Sense

Mathematics, 2018
It is well known that the Black-Scholes model is used to establish the behavior of the option pricing in the financial market. In this paper, we propose the modified version of Black-Scholes model with two assets based on the Liouville-Caputo fractional ...
P. Sawangtong, Kamonchat Trachoo, Wannika Sawangtong, Benchawan Wiwattanapataphee   +3 more
semanticscholar   +1 more source

A discrete spectral method for time fractional fourth-order 2D diffusion-wave equation involving ψ-Caputo fractional derivative

Results in Applied Mathematics
In this work, the ψ-Caputo fractional derivative, as a generalization of the classical Caputo fractional derivative in which the fractional derivative of a sufficiently differentiable function is defined with respect to another strictly increasing ...
M.H. Heydari, M. Razzaghi
doaj   +1 more source

On the stable numerical evaluation of caputo fractional derivatives

Computers & Mathematics with Applications, 2006
AbstractThe computation of Caputo's fractional derivatives in the presence of measured data is considered as an ill-posed problem and treated by mollification techniques. It is shown that, with the appropriate choice of the radius of mollification, the method is a regularizing algorithm, and the order of convergence is derived.
openaire   +2 more sources

A Novel Fractional‐Order Predictive PI Controller Approach for the Systems With Noninteger Order Delay

Optimal Control Applications and Methods, EarlyView.
Hybrid Algorithm‐Based Optimal FOPI Controller in Three‐phase UPQC system ABSTRACT Time delay (TD) is a common phenomenon in practical systems. Most studies have focused on the classical notion of integer‐order TD. However, it should not be neglected that the delay can also be noninteger.
Erdinç Şahin
wiley   +1 more source

A normalized Caputo–Fabrizio fractional diffusion equation

AIMS Mathematics
We propose a normalized Caputo–Fabrizio (CF) fractional diffusion equation. The CF fractional derivative replaces the power-law kernel in the Caputo derivative with an exponential kernel, which avoids singularities. Compared to the Caputo derivative, the
Junseok Kim
doaj   +1 more source