Special Issue "Fractional Differential and Partial Differential Systems with Applications"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".

Deadline for manuscript submissions: closed (29 February 2020).

Special Issue Editor

Prof. Dr. Dimplekumar N. Chalishajar
E-Mail Website
Guest Editor
Department of Applied Mathematics, Virginia Military Institute, 435 Mallory Hall, Letcher Av., Lexington, VA 24450, USA
Interests: control theory; dynamical system; fractional order systems; delay systems; stochastic system; partial differential equation
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Special Issue Information

Dear Colleagues,

It is well known that fractional calculus has been recognized since regular calculus, with the first written reference dating back to September 1695 in letter from Leibniz to L’Hospital. In recent years, various families of fractional-order systems have been found to be remarkably important and fruitful, mainly due to their demonstrated applications in numerous seemingly diverse and widespread areas of the mathematical, physical, chemical, engineering, rubber technology, robotics, and statistical sciences. Many of these fractional-order systems provide interesting, potentially useful tools for solving ordinary and partial differential equations, as well as integral and integro-differential equations; fractional-calculus analogues and extensions of each of these equations; and various other problems involving special functions of mathematical physics and applied mathematics, as well as their extensions and generalizations in one or more variables. Moreover, fractional calculus plays an important role even in complex systems, and therefore allows us to use a better description of some real-world phenomena. Based on this fact, the fractional order systems are ubiquitous, and the whole real world around us is a fractional, not integer one. Because of this, it is urgent consider almost all systems as fractional order systems. 

In this Special Issue, we invite and welcome reviews, and expository and original research articles dealing with recent advances in the theory of fractional-order systems and their multidisciplinary applications.

Prof. Dr. Dimplekumar N. Chalishajar
Guest Editor

Manuscript Submission Information

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Keywords

  • dynamical and stochastic systems based upon fractional calculus
  • operators of fractional calculus and their applications
  • fractional-order ODEs and PDEs
  • fractional calculus and its applications
  • fractional-order integro-differential equations
  • fixed point theory and monotone operator theory
  • finite/infinite time/state delay systems/inclusions with set valued analysis
  • numerical estimation of fractional order systems

Published Papers (5 papers)

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Research

Open AccessArticle
Dynamics of General Class of Difference Equations and Population Model with Two Age Classes
Mathematics 2020, 8(4), 516; https://doi.org/10.3390/math8040516 - 03 Apr 2020
Cited by 3 | Viewed by 449
Abstract
In this paper, we study the qualitative behavior of solutions for a general class of difference equations. The criteria of local and global stability, boundedness and periodicity character (with period 2k) of the solution are established. Moreover, by applying our general [...] Read more.
In this paper, we study the qualitative behavior of solutions for a general class of difference equations. The criteria of local and global stability, boundedness and periodicity character (with period 2 k ) of the solution are established. Moreover, by applying our general results on a population model with two age classes, we establish the qualitative behavior of solutions of this model. To support our results, we introduce some numerical examples. Full article
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Open AccessArticle
Positive Solutions for a Class of p-Laplacian Hadamard Fractional-Order Three-Point Boundary Value Problems
Mathematics 2020, 8(3), 308; https://doi.org/10.3390/math8030308 - 27 Feb 2020
Cited by 10 | Viewed by 562
Abstract
In this paper, using the Avery–Henderson fixed point theorem and the monotone iterative technique, we investigate the existence of positive solutions for a class of p-Laplacian Hadamard fractional-order three-point boundary value problems. Full article
Open AccessArticle
Sufficient Criteria for the Absence of Global Solutions for an Inhomogeneous System of Fractional Differential Equations
Mathematics 2020, 8(1), 9; https://doi.org/10.3390/math8010009 - 19 Dec 2019
Viewed by 393
Abstract
A nonlinear inhomogeneous system of fractional differential equations is investigated. Namely, sufficient criteria are obtained so that the considered system has no global solutions. Furthermore, an example is provided to show the effect of the inhomogeneous terms on the blow-up of solutions. Our [...] Read more.
A nonlinear inhomogeneous system of fractional differential equations is investigated. Namely, sufficient criteria are obtained so that the considered system has no global solutions. Furthermore, an example is provided to show the effect of the inhomogeneous terms on the blow-up of solutions. Our results are extensions of those obtained by Furati and Kirane (2008) in the homogeneous case. Full article
Open AccessArticle
Simplified Fractional Order Controller Design Algorithm
Mathematics 2019, 7(12), 1166; https://doi.org/10.3390/math7121166 - 02 Dec 2019
Cited by 6 | Viewed by 613
Abstract
Classical fractional order controller tuning techniques usually establish the parameters of the controller by solving a system of nonlinear equations resulted from the frequency domain specifications like phase margin, gain crossover frequency, iso-damping property, robustness to uncertainty, etc. In the present paper a [...] Read more.
Classical fractional order controller tuning techniques usually establish the parameters of the controller by solving a system of nonlinear equations resulted from the frequency domain specifications like phase margin, gain crossover frequency, iso-damping property, robustness to uncertainty, etc. In the present paper a novel fractional order generalized optimum method for controller design using frequency domain is presented. The tuning rules are inspired from the symmetrical optimum principles of Kessler. In the first part of the paper are presented the generalized tuning rules of this method. Introducing the fractional order, one more degree of freedom is obtained in design, offering solution for practically any desired closed-loop performance measures. The proposed method has the advantage that takes into account both robustness aspects and desired closed-loop characteristics, using simple tuning-friendly equations. It can be applied to a wide range of process models, from integer order models to fractional order models. Simulation results are given to highlight these advantages. Full article
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Open AccessArticle
An Analytical Technique to Solve the System of Nonlinear Fractional Partial Differential Equations
Mathematics 2019, 7(6), 505; https://doi.org/10.3390/math7060505 - 02 Jun 2019
Cited by 11 | Viewed by 1578
Abstract
The Kortweg–de Vries equations play an important role to model different physical phenomena in nature. In this research article, we have investigated the analytical solution to system of nonlinear fractional Kortweg–de Vries, partial differential equations. The Caputo operator is used to define fractional [...] Read more.
The Kortweg–de Vries equations play an important role to model different physical phenomena in nature. In this research article, we have investigated the analytical solution to system of nonlinear fractional Kortweg–de Vries, partial differential equations. The Caputo operator is used to define fractional derivatives. Some illustrative examples are considered to check the validity and accuracy of the proposed method. The obtained results have shown the best agreement with the exact solution for the problems. The solution graphs are in full support to confirm the authenticity of the present method. Full article
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