Ioannis Dassios
YOU?
Author Swipe
View article: ON SYSTEMS OF DOUBLE-INDEX LINEAR DIFFERENCE EQUATIONS
ON SYSTEMS OF DOUBLE-INDEX LINEAR DIFFERENCE EQUATIONS Open
In this article, we introduce a family of double-index linear difference equations and develop a framework for their analysis by defining appropriate operators. These operators are used to derive explicit general solutions and to study the…
View article: Advanced computational methods and innovative applications in science and engineering
Advanced computational methods and innovative applications in science and engineering Open
The Special Issue has aimed to publish selected high-quality papers presented at the “Third International Conference on Applied Mathematics in Engineering (ICAME'24),” which was held from June 26 to 28, 2024, at VE Hotels, Ayvalık, Balıkes…
View article: The Collocation Method Based on the New Chebyshev Cardinal Functions for Solving Fractional Delay Differential Equations
The Collocation Method Based on the New Chebyshev Cardinal Functions for Solving Fractional Delay Differential Equations Open
The Chebyshev cardinal functions based on the Lobatto grid are introduced and used for the first time to solve the fractional delay differential equations. The presented algorithm is based on the collocation method, which is applied to sol…
View article: A Novel and Accurate Algorithm for Solving Fractional Diffusion-Wave Equations
A Novel and Accurate Algorithm for Solving Fractional Diffusion-Wave Equations Open
The main objective of this work is to apply a novel and accurate algorithm for solving the second-order and fourth-order fractional diffusion-wave equations (FDWEs). First, the desired equation is reduced to the corresponding Volterra inte…
View article: Significance of Mathematical Modeling and Control in Real-World Problems: New Developments and Applications
Significance of Mathematical Modeling and Control in Real-World Problems: New Developments and Applications Open
Mathematical modeling and system control are employed in many research problems, ranging from physical and chemical processes to biomathematics and life sciences [...]
View article: Constructing Electricity Market Models
Constructing Electricity Market Models Open
This working paper presents a comprehensive study on the development and analysis of various electricity market models, focusing on continuous, discrete, and fractional-order approaches. The continuous model captures the ongoing interactio…
View article: A discrete model for force-based elasticity and plasticity
A discrete model for force-based elasticity and plasticity Open
The article presents a mathematical model that simulates the elastic and plastic behaviour of discrete systems representing isotropic materials. The systems consist of one lattice of nodes connected by edges and a second lattice with nodes…
View article: Instantaneous Power Theory Revisited with Classical Mechanics
Instantaneous Power Theory Revisited with Classical Mechanics Open
The paper revisits the concepts of instantaneous active and reactive powers and provides a novel definition for basic circuit elements based on quantities utilized in classical mechanics, such as absolute and relative velocity, momentum de…
View article: A discussion of stability analysis for systems of differential equations with multiple and distributed delays
A discussion of stability analysis for systems of differential equations with multiple and distributed delays Open
In this article, we consider a class of systems of multiple delay differential equations (MDDEs). We first define a characteristic matrix equation that can be used to analyze the stability of the equilibrium of a system of MDDEs. Then we c…
View article: A bounded dynamical network of curves and the stability of its steady states
A bounded dynamical network of curves and the stability of its steady states Open
In this article, we study the dynamic behavior of a network that consists of curves that are in motion and bounded. We first focus on the construction of the model which is a system of nonlinear partial differential equations (PDEs). This …
View article: On the relations between a singular system of differential equations and a system with delays
On the relations between a singular system of differential equations and a system with delays Open
In this article, we consider a class of systems of differential equations with multiple delays. We define a transform that reformulates the system with delays into a singular linear system of differential equations whose coefficients are n…
View article: Micro-flexibility: Challenges for power system modeling and control
Micro-flexibility: Challenges for power system modeling and control Open
This paper collects the challenges and opportunities that emerge from the millions of controllable devices – and the micro-flexibility they offer – that are deployed across the transmission and distribution systems. Moving to power systems…
View article: The Fractional Investigation of Some Nonlinear Partial Differential Equations by Using an Efficient Procedure
The Fractional Investigation of Some Nonlinear Partial Differential Equations by Using an Efficient Procedure Open
The nonlinearity in many problems occurs because of the complexity of the given physical phenomena. The present paper investigates the non-linear fractional partial differential equations’ solutions using the Caputo operator with Laplace r…
View article: A Reliable Technique for Solving Fractional Partial Differential Equation
A Reliable Technique for Solving Fractional Partial Differential Equation Open
The development of numeric-analytic solutions and the construction of fractional-order mathematical models for practical issues are of the greatest importance in a variety of applied mathematics, physics, and engineering problems. The Lapl…
View article: Frequency Divider as a Continuum
Frequency Divider as a Continuum Open
The letter describes a novel, continuum-based approach, to capture the evolution of electromechanical dynamics in a power network following a disturbance. Such approach is based on the frequency divider formula (FDF), which was recently pr…
View article: Moore–Gibson–Thompson Thermoelastic Model Effect of Laser-Induced Microstructures of a Microbeam Sitting on Visco-Pasternak Foundations
Moore–Gibson–Thompson Thermoelastic Model Effect of Laser-Induced Microstructures of a Microbeam Sitting on Visco-Pasternak Foundations Open
Due to the intricacy of this topic, the thermal study of microstructures on triple-parameter foundations subjected to ultrafast laser pulses has not received much attention. It is necessary to determine the thermal performance of a structu…
View article: Motion along a Space Curve with a Quasi-Frame in Euclidean 3-Space: Acceleration and Jerk
Motion along a Space Curve with a Quasi-Frame in Euclidean 3-Space: Acceleration and Jerk Open
The resolution of the acceleration and jerk vectors of a particle moving on a space curve in the Euclidean 3-space is considered. By applying this resolution and Siacci’s theorem, alternative resolutions of acceleration and jerk vectors ar…
View article: Small-signal stability analysis of implicit integration methods for power systems with delays
Small-signal stability analysis of implicit integration methods for power systems with delays Open
The paper focuses on the accuracy and stability of implicit numerical methods when utilized for the Time Domain Integration (TDI) of power systems with inclusion of time delays. In particular, a small-disturbance analysis technique is prop…
View article: A New Modified Analytical Approach for the Solution of Time-Fractional Convection–Diffusion Equations With Variable Coefficients
A New Modified Analytical Approach for the Solution of Time-Fractional Convection–Diffusion Equations With Variable Coefficients Open
In this article, a new modification of the Adomian decomposition method is performed for the solution fractional order convection–diffusion equation with variable coefficient and initial–boundary conditions. The solutions of the suggested …
View article: Power system modelling as stochastic functional hybrid differential‐algebraic equations
Power system modelling as stochastic functional hybrid differential‐algebraic equations Open
This paper presents the software tools developed for the research project Advanced Modelling for Power System Analysis and Simulation (AMPSAS) funded by Science Foundation Ireland from 2016 to 2021. The main objective of AMPSAS was the dev…
View article: A Biorthogonal Hermite Cubic Spline Galerkin Method for Solving Fractional Riccati Equation
A Biorthogonal Hermite Cubic Spline Galerkin Method for Solving Fractional Riccati Equation Open
This paper is devoted to the wavelet Galerkin method to solve the Fractional Riccati equation. To this end, biorthogonal Hermite cubic Spline scaling bases and their properties are introduced, and the fractional integral is represented bas…
View article: On the Wavelet Collocation Method for Solving Fractional Fredholm Integro-Differential Equations
On the Wavelet Collocation Method for Solving Fractional Fredholm Integro-Differential Equations Open
An efficient algorithm is proposed to find an approximate solution via the wavelet collocation method for the fractional Fredholm integro-differential equations (FFIDEs). To do this, we reduce the desired equation to an equivalent linear o…
View article: An Efficient Technique of Fractional-Order Physical Models Involving ρ-Laplace Transform
An Efficient Technique of Fractional-Order Physical Models Involving ρ-Laplace Transform Open
In this article, the ρ-Laplace transform is paired with a new iterative method to create a new hybrid methodology known as the new iterative transform method (NITM). This method is applied to analyse fractional-order third-order dispersive…
View article: Singular over-determined systems of linear differential equations
Singular over-determined systems of linear differential equations Open
We study a class of singular over-determined systems of differential equations and firstly prove that there exist solutions under certain conditions. For the case of existence we provide closed formulas of solutions and based on the spectr…
View article: Small-Signal Stability Analysis of Numerical Integration Methods
Small-Signal Stability Analysis of Numerical Integration Methods Open
The paper provides a novel framework to study the accuracy and stability of numerical integration schemes when employed for the time domain simulation of power systems. A matrix pencil-based approach is adopted to evaluate the error betwee…
View article: Using Differential Geometry to Revisit the Paradoxes of the Instantaneous Frequency
Using Differential Geometry to Revisit the Paradoxes of the Instantaneous Frequency Open
This paper proposes a general framework to interpret the concept of Instantaneous Frequency (IF) in three-phase systems. The paper first recalls the conventional frequency-domain analysis based on the Fourier transform as well as the defin…
View article: Using Differential Geometry to Revisit the Paradoxes of the Instantaneous Frequency
Using Differential Geometry to Revisit the Paradoxes of the Instantaneous Frequency Open
This paper proposes a general framework to interpret the concept of Instantaneous Frequency (IF) in three-phase systems. The paper first recalls the conventional frequency-domain analysis based on the Fourier transform as well as the defin…
View article: Pseudospectral Method Based on Müntz–Legendre Wavelets for Solving the Abel Integral Equation
Pseudospectral Method Based on Müntz–Legendre Wavelets for Solving the Abel Integral Equation Open
This paper deals with the numerical solution of the Abel integral equation based on Müntz–Legendre wavelets. To this end, the Abel integral operator is represented by Müntz–Legendre wavelets as an operational matrix. To find this matrix, w…
View article: Applications of the Frenet Frame to Electric Circuits
Applications of the Frenet Frame to Electric Circuits Open
The paper discusses the relationships between electrical quantities, such as voltages, currents, and frequency, and geometrical ones, namely curvature and torsion. The proposed approach is based on the Frenet frame utilized in differential…
View article: Differential/Difference Equations: Mathematical Modeling, Oscillation and Applications
Differential/Difference Equations: Mathematical Modeling, Oscillation and Applications Open
The study of oscillatory phenomena is an important part of the theory of differential equations. Oscillations naturally occur in virtually every area of applied science including, e.g., mechanics, electrical, radio engineering, and vibrote…