Random fractional generalized Airy differential equations: a probabilistic analysis using mean square calculus
The aim of this paper is to study a generalization of fractional Airy differential equations
whose input data (coefficient and initial conditions) are random variables. Under appropriate …
whose input data (coefficient and initial conditions) are random variables. Under appropriate …
[HTML][HTML] Investigation on Ginzburg-Landau equation via a tested approach to benchmark stochastic Davis-Skodje system
We propose new numerical methods with adding a modified ordinary differential equation
solver to the Milstein methods for solution of stiff stochastic systems. We study a general form …
solver to the Milstein methods for solution of stiff stochastic systems. We study a general form …
[HTML][HTML] Mean square convergent numerical solutions of random fractional differential equations: Approximations of moments and density
A fractional forward Euler-like method is developed to solve initial value problems with
uncertainties formulated via the Caputo fractional derivative. The analysis is conducted by …
uncertainties formulated via the Caputo fractional derivative. The analysis is conducted by …
Mean square calculus and random linear fractional differential equations: Theory and applications
The aim of this paper is to study, in mean square sense, a class of random fractional linear
differential equation where the initial condition and the forcing term are assumed to be …
differential equation where the initial condition and the forcing term are assumed to be …
Modified stochastic theta methods by ODEs solvers for stochastic differential equations
In this paper, we present a family of stochastic theta methods modified by ODEs solvers for
stochastic differential equations. This class of methods constructed by adding error …
stochastic differential equations. This class of methods constructed by adding error …
Extending the deterministic Riemann–Liouville and Caputo operators to the random framework: A mean square approach with applications to solve random fractional …
This paper extends both the deterministic fractional Riemann–Liouville integral and the
Caputo fractional derivative to the random framework using the mean square random …
Caputo fractional derivative to the random framework using the mean square random …
Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties
J Calatayud, JC Cortés, M Jornet… - Advances in Difference …, 2018 - Springer
In this paper we study random non-autonomous second order linear differential equations
by taking advantage of the powerful theory of random difference equations. The coefficients …
by taking advantage of the powerful theory of random difference equations. The coefficients …
Improved Euler–Maruyama method for numerical solution of the Itô stochastic differential systems by composite previous-current-step idea
In this paper, by composite previous-current-step idea, we propose two numerical schemes
for solving the Itô stochastic differential systems. Our approaches, which are based on the …
for solving the Itô stochastic differential systems. Our approaches, which are based on the …
Solving random homogeneous linear second-order differential equations: a full probabilistic description
In this paper a complete probabilistic description for the solution of random homogeneous
linear second-order differential equations via the computation of its two first probability …
linear second-order differential equations via the computation of its two first probability …
Solving the stochastic differential systems with modified split-step Euler-Maruyama method
A new category of the split-step Euler-Maruyama types schemes are constructed to study the
stochastic differential systems. Under given conditions, we analyze the mean-square …
stochastic differential systems. Under given conditions, we analyze the mean-square …