Special Issue "Mathematical Modeling using Differential Equations, and Network Theory"

A special issue of Applied Sciences (ISSN 2076-3417).

Deadline for manuscript submissions: closed (31 December 2019).

Special Issue Editor

Dr. Ioannis Dassios
E-Mail Website
Guest Editor
ESIPP, University College Dublin, Ireland
Interests: Differential/Difference equations, Dynamical systems, Modelling and Stability Analysis of Electric Power Systems, Mathematics of Networks, Fractional calculus, Mathematical modelling (Power Systems, Materials Science, Energy, Macroeconomics, Social Media, etc),Optimization for the analysis of large scale data sets, Fluid Mechanics, Discrete calculus, Bayes Control, E-learning
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Special Issue Information

Dear Colleagues,

This special issue aims at collecting latest results on Differential/Difference Equations, Mathematics of Networks, and their applications into Electrical Power Systems, Materials, Energy, Macroeconomics, etc.

This Special Issue will accept high-quality papers having original research results, and its purpose is to bring together Mathematicians with Physicists, Engineers, as well as other scientists.

Topics covered but not limited to:

  • Differential/Difference equations
  • Dynamical systems
  • Mathematics of Networks
  • Fractional calculus
  • Modelling and Stability Analysis of Power Systems
  • Discrete calculus
  • Circuits Theory
  • Signal Processing
  • Materials Science
  • Energy Systems
  • Macroeconomics

Dr. Ioannis Dassios
Guest Editor

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Published Papers (8 papers)

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Research

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Open AccessArticle
Fractional View Analysis of Acoustic Wave Equations, Using Fractional-Order Differential Equations
Appl. Sci. 2020, 10(2), 610; https://doi.org/10.3390/app10020610 - 15 Jan 2020
Abstract
In the present research work, a newly developed technique which is known as variational homotopy perturbation transform method is implemented to solve fractional-order acoustic wave equations. The basic idea behind the present research work is to extend the variational homotopy perturbation method to [...] Read more.
In the present research work, a newly developed technique which is known as variational homotopy perturbation transform method is implemented to solve fractional-order acoustic wave equations. The basic idea behind the present research work is to extend the variational homotopy perturbation method to variational homotopy perturbation transform method. The proposed scheme has confirmed, that it is an accurate and straightforward technique to solve fractional-order partial differential equations. The validity of the method is verified with the help of some illustrative examples. The obtained solutions have shown close contact with the exact solutions. Furthermore, the highest degree of accuracy has been achieved by the suggested method. In fact, the present method can be considered as one of the best analytical techniques compared to other analytical techniques to solve non-linear fractional partial differential equations. Full article
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Open AccessArticle
Analytical Solutions of (2+Time Fractional Order) Dimensional Physical Models, Using Modified Decomposition Method
Appl. Sci. 2020, 10(1), 122; https://doi.org/10.3390/app10010122 - 23 Dec 2019
Abstract
In this article, a new analytical technique based on an innovative transformation is used to solve (2+time fractional-order) dimensional physical models. The proposed method is the hybrid methodology of Shehu transformation along with Adomian decomposition method. The series form solution is obtained by [...] Read more.
In this article, a new analytical technique based on an innovative transformation is used to solve (2+time fractional-order) dimensional physical models. The proposed method is the hybrid methodology of Shehu transformation along with Adomian decomposition method. The series form solution is obtained by using the suggested method which provides the desired rate of convergence. Some numerical examples are solved by using the proposed method. The solutions of the targeted problems are represented by graphs which have confirmed closed contact between the exact and obtained solutions of the problems. Based on the novelty and straightforward implementation of the method, it is considered to be one of the best analytical techniques to solve linear and non-linear fractional partial differential equations. Full article
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Open AccessArticle
Multi-Switching Combination Synchronization of Three Fractional-Order Delayed Systems
Appl. Sci. 2019, 9(20), 4348; https://doi.org/10.3390/app9204348 - 15 Oct 2019
Abstract
Multi-switching combination synchronization of three fractional-order delayed systems is investigated. This is a generalization of previous multi-switching combination synchronization of fractional-order systems by introducing time-delays. Based on the stability theory of linear fractional-order systems with multiple time-delays, we propose appropriate controllers to obtain [...] Read more.
Multi-switching combination synchronization of three fractional-order delayed systems is investigated. This is a generalization of previous multi-switching combination synchronization of fractional-order systems by introducing time-delays. Based on the stability theory of linear fractional-order systems with multiple time-delays, we propose appropriate controllers to obtain multi-switching combination synchronization of three non-identical fractional-order delayed systems. In addition, the results of our numerical simulations show that they are in accordance with the theoretical analysis. Full article
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Open AccessArticle
Parametrical Non-Complex Tests to Evaluate Partial Decentralized Linear-Output Feedback Control Stabilization Conditions from Their Centralized Stabilization Counterparts
Appl. Sci. 2019, 9(9), 1739; https://doi.org/10.3390/app9091739 - 26 Apr 2019
Cited by 2
Abstract
This paper formulates sufficiency-type linear-output feedback decentralized closed-loop stabilization conditions if the continuous-time linear dynamic system can be stabilized under linear output-feedback centralized stabilization. The provided tests are simple to evaluate, while they are based on the quantification of the sufficiently smallness of [...] Read more.
This paper formulates sufficiency-type linear-output feedback decentralized closed-loop stabilization conditions if the continuous-time linear dynamic system can be stabilized under linear output-feedback centralized stabilization. The provided tests are simple to evaluate, while they are based on the quantification of the sufficiently smallness of the parametrical error norms between the control, output, interconnection and open-loop system dynamics matrices and the corresponding control gains in the decentralized case related to the centralized counterpart. The tolerance amounts of the various parametrical matrix errors are described by the maximum allowed tolerance upper-bound of a small positive real parameter that upper-bounds the various parametrical error norms. Such a tolerance is quantified by considering the first or second powers of such a small parameter. The results are seen to be directly extendable to quantify the allowed parametrical errors that guarantee the closed-loop linear output-feedback stabilization of a current system related to its nominal counterpart. Furthermore, several simulated examples are also discussed. Full article
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Open AccessArticle
Transient-Flow Modeling of Vertical Fractured Wells with Multiple Hydraulic Fractures in Stress-Sensitive Gas Reservoirs
Appl. Sci. 2019, 9(7), 1359; https://doi.org/10.3390/app9071359 - 31 Mar 2019
Cited by 1
Abstract
Massive hydraulic fracturing of vertical wells has been extensively employed in the development of low-permeability gas reservoirs. The existence of multiple hydraulic fractures along a vertical well makes the pressure profile around the vertical well complex. This paper studies the pressure dependence of [...] Read more.
Massive hydraulic fracturing of vertical wells has been extensively employed in the development of low-permeability gas reservoirs. The existence of multiple hydraulic fractures along a vertical well makes the pressure profile around the vertical well complex. This paper studies the pressure dependence of permeability to develop a seepage model of vertical fractured wells with multiple hydraulic fractures. Both transformed pseudo-pressure and perturbation techniques have been employed to linearize the proposed model. The superposition principle and a hybrid analytical-numerical method were used to obtain the bottom-hole pseudo-pressure solution. Type curves for pseudo-pressure are presented and identified. The effects of the relevant parameters (such as dimensionless permeability modulus, fracture conductivity coefficient, hydraulic-fracture length, angle between the two adjacent hydraulic fractures, the difference of the hydraulic-fracture lengths, and hydraulic-fracture number) on the type curve and the error caused by neglecting the stress sensitivity are discussed in detail. The proposed work can enrich the understanding of the influence of the stress sensitivity on the performance of a vertical fractured well with multiple hydraulic fractures and can be used to more accurately interpret and forecast the transient pressure. Full article
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Open AccessArticle
Policy-Compliant Maximum Network Flows
Appl. Sci. 2019, 9(5), 863; https://doi.org/10.3390/app9050863 - 28 Feb 2019
Abstract
Computer network administrators are often interested in the maximal bandwidth that can be achieved between two nodes in the network, or how many edges can fail before the network gets disconnected. Classic maximum flow algorithms that solve these problems are well-known. However, in [...] Read more.
Computer network administrators are often interested in the maximal bandwidth that can be achieved between two nodes in the network, or how many edges can fail before the network gets disconnected. Classic maximum flow algorithms that solve these problems are well-known. However, in practice, network policies are in effect, severely restricting the flow that can actually be set up. These policies are put into place to conform to service level agreements and optimize network throughput, and can have a large impact on the actual routing of the flows. In this work, we model the problem and define a series of progressively more complex conditions and algorithms that calculate increasingly tighter bounds on the policy-compliant maximum flow using regular expressions and finite state automata. To the best of our knowledge, this is the first time that specific conditions are deduced, which characterize how to calculate policy-compliant maximum flows using classic algorithms on an unmodified network. Full article
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Open AccessArticle
The Fractional Form of the Tinkerbell Map Is Chaotic
Appl. Sci. 2018, 8(12), 2640; https://doi.org/10.3390/app8122640 - 16 Dec 2018
Cited by 6
Abstract
This paper is concerned with a fractional Caputo-difference form of the well-known Tinkerbell chaotic map. The dynamics of the proposed map are investigated numerically through phase plots, bifurcation diagrams, and Lyapunov exponents considered from different perspectives. In addition, a stabilization controller is proposed, [...] Read more.
This paper is concerned with a fractional Caputo-difference form of the well-known Tinkerbell chaotic map. The dynamics of the proposed map are investigated numerically through phase plots, bifurcation diagrams, and Lyapunov exponents considered from different perspectives. In addition, a stabilization controller is proposed, and the asymptotic convergence of the states is established by means of the stability theory of linear fractional discrete systems. Numerical results are employed to confirm the analytical findings. Full article
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Review

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Open AccessReview
Short Overview of Early Developments of the Hardy Cross Type Methods for Computation of Flow Distribution in Pipe Networks
Appl. Sci. 2019, 9(10), 2019; https://doi.org/10.3390/app9102019 - 16 May 2019
Cited by 3
Abstract
Hardy Cross originally proposed a method for analysis of flow in networks of conduits or conductors in 1936. His method was the first really useful engineering method in the field of pipe network calculation. Only electrical analogs of hydraulic networks were used before [...] Read more.
Hardy Cross originally proposed a method for analysis of flow in networks of conduits or conductors in 1936. His method was the first really useful engineering method in the field of pipe network calculation. Only electrical analogs of hydraulic networks were used before the Hardy Cross method. A problem with flow resistance versus electrical resistance makes these electrical analog methods obsolete. The method by Hardy Cross is taught extensively at faculties, and it remains an important tool for the analysis of looped pipe systems. Engineers today mostly use a modified Hardy Cross method that considers the whole looped network of pipes simultaneously (use of these methods without computers is practically impossible). A method from a Russian practice published during the 1930s, which is similar to the Hardy Cross method, is described, too. Some notes from the work of Hardy Cross are also presented. Finally, an improved version of the Hardy Cross method, which significantly reduces the number of iterations, is presented and discussed. We also tested multi-point iterative methods, which can be used as a substitution for the Newton–Raphson approach used by Hardy Cross, but in this case this approach did not reduce the number of iterations. Although many new models have been developed since the time of Hardy Cross, the main purpose of this paper is to illustrate the very beginning of modeling of gas and water pipe networks and ventilation systems. As a novelty, a new multi-point iterative solver is introduced and compared with the standard Newton–Raphson iterative method. Full article
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