Random fractional generalized Airy differential equations: a probabilistic analysis using mean square calculus

C Burgos, JC Cortés, A Debbouche, L Villafuerte… - Applied Mathematics …, 2019 - Elsevier
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 …

[HTML][HTML] Investigation on Ginzburg-Landau equation via a tested approach to benchmark stochastic Davis-Skodje system

K Nouri, H Ranjbar, D Baleanu, L Torkzadeh - Alexandria Engineering …, 2021 - Elsevier
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 …

[HTML][HTML] Mean square convergent numerical solutions of random fractional differential equations: Approximations of moments and density

C Burgos, JC Cortés, L Villafuerte… - Journal of Computational …, 2020 - Elsevier
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 …

Mean square calculus and random linear fractional differential equations: Theory and applications

C Burgos, JC Cortés, L Villafuerte… - … and Nonlinear Sciences, 2017 - sciendo.com
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 …

Modified stochastic theta methods by ODEs solvers for stochastic differential equations

K Nouri, H Ranjbar, L Torkzadeh - Communications in Nonlinear Science …, 2019 - Elsevier
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 …

Extending the deterministic Riemann–Liouville and Caputo operators to the random framework: A mean square approach with applications to solve random fractional …

C Burgos, JC Cortés, L Villafuerte… - Chaos, Solitons & …, 2017 - Elsevier
This paper extends both the deterministic fractional Riemann–Liouville integral and the
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 …

Improved Euler–Maruyama method for numerical solution of the Itô stochastic differential systems by composite previous-current-step idea

K Nouri, H Ranjbar, L Torkzadeh - Mediterranean Journal of Mathematics, 2018 - Springer
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 …

Solving random homogeneous linear second-order differential equations: a full probabilistic description

MC Casabán, JC Cortés, JV Romero… - Mediterranean Journal of …, 2016 - Springer
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 …

Solving the stochastic differential systems with modified split-step Euler-Maruyama method

K Nouri, H Ranjbar, L Torkzadeh - Communications in Nonlinear Science …, 2020 - Elsevier
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 …