Alexandra Galhano's research works | University of Porto, Porto (UP) and other places

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Fractional Stochastic Partial Differential Equations: Numerical Advances and Practical Applications—A State of the Art Review

Article

Full-text available

May 2024

This article aims to provide a comprehensive review of the latest advancements in numerical methods and practical implementations in the field of fractional stochastic partial differential equations (FSPDEs). This type of equation integrates fractional calculus, stochastic processes, and differential equations to model complex dynamical systems cha...

Special Issue - "Complexity, Fractality and Fractional Dynamics Applied to Science and Engineering" - Fractal and Fractional (ISSN 2504-3110)

Research Proposal

Aug 2023

Special Issue Information Fractal and Fractional (ISSN 2504-3110) https://www.mdpi.com/journal/fractalfract/special_issues/9K10NKTKAW This SI is now open for submission.Deadline for manuscript submissions: 31 Oct 2024. Many problems in classical and quantum physics, statistical physics, engineering, biology, psychology, economics, and finance are...

A Matrix Transform Technique for Distributed-Order Time-Fractional Advection–Dispersion Problems

Article

Full-text available

Jun 2023

Invoking the matrix transfer technique, we propose a novel numerical scheme to solve the time-fractional advection–dispersion equation (ADE) with distributed-order Riesz-space fractional derivatives (FDs). The method adopts the midpoint rule to reformulate the distributed-order Riesz-space FDs by means of a second-order linear combination of Riesz-...

Figure 1. Inverted pendulum schematic chart stabilized by means of wain...

Example 2: The values of ¯ E ms , ECO ms and CPU time (expressed in...

The approximated SI values concerning the 50 simulated paths for (14),...

A Numerical Algorithm for Solving Nonlocal Nonlinear Stochastic Delayed Systems with Variable-Order Fractional Brownian Noise

Article

Full-text available

Mar 2023

A numerical technique was developed for solving nonlocal nonlinear stochastic delayed differential equations driven by fractional variable-order Brownian noise. Error analysis of the proposed technique was performed and discussed. The method was applied to the nonlocal stochastic fluctuations of the human body and the Nicholson’s blowfly models, an...

Hybridization of Block-Pulse and Taylor Polynomials for Approximating 2D Fractional Volterra Integral Equations

Article

Full-text available

Sep 2022

This paper proposes an accurate numerical approach for computing the solution of twodimensional fractional Volterra integral equations. The operational matrices of fractional integration based on the Hybridization of block-pulse and Taylor polynomials are implemented to transform these equations into a system of linear algebraic equations. The erro...