Forthcoming and Online First Articles

International Journal of Dynamical Systems and Differential Equations

International Journal of Dynamical Systems and Differential Equations (IJDSDE)

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International Journal of Dynamical Systems and Differential Equations (5 papers in press)

Regular Issues

  • Pseudo periodicity and pseudo almost periodicity in shifts   Order a copy of this article
    by Meng Hu, Lili Wang 
    Abstract: By means of the shifts operators
    Keywords: Pseudo periodicity; Pseudo almost periodicity; Shift operator; Time scale.
    DOI: 10.1504/IJDSDE.2023.10060882
     
  • The limit cycles of a class of discontinuous piecewise differential systems   Order a copy of this article
    by Louiza Baymout, Rebiha Benterki, Jaume Llibre 
    Abstract: The determination of the maximum number of limit cycles and their possible positions in the plane is one of the most difficult problems in the qualitative theory of planar differential systems. This problem is related to the second part of the unsolved 16th Hilberts problem. Due to their applications in modelling many natural phenomena, piecewise differential systems have recently attracted big attention. The upper bound number of limit cycles that a class of differential systems may exhibit is typically very difficult to determine. In this work we extend the second part of the 16th Hilberts problem to the planar discontinuous piecewise differential systems separated by a straight line and formed by an arbitrary linear centre and an arbitrary cubic uniform isochronous centre. We provide for this class of piecewise differential systems an upper bound on its maximal number of limit cycles, and we prove that such an upper bound is reached.
    Keywords: Cubic uniform isochronous center; linear center; limit cycle; discontinuous piecewise differential system.
    DOI: 10.1504/IJDSDE.2023.10061493
     
  • The Appropriate Expression and Non-Uniqueness of Solution for Impulsive Katugampola Fractional Order System   Order a copy of this article
    by Xianmin Zhang, Zuohua Liu, Yali He, Zuming Peng, Shixian Yang 
    Abstract: For two impulsive generalised fractional order systems (IGFrOSs), we consider their conditions of fractional derivative and fractional integral by two new fractional order properties of piecewise function to find that the equivalent integral equations (EIEs) of the IGFrOSs are a combination of two integral equations ((t) and j(t)) with an arbitrary constant to reveal the non-uniqueness of the IGFrOSs solution, and moreover, we give the appropriate expressions of the EIEs to easily verify that the EIEs satisfy the conditions of fractional derivative and fractional integral in the two IGFrOSs. Finally, we apply two numerical models to illustrate the EIEs and the non-uniqueness of solution of two IGFrOSs.
    Keywords: impulsive fractional differential equations; equivalent integral equations; initial value problems; non-uniqueness of solution.
    DOI: 10.1504/IJDSDE.2024.10064818
     
  • Group Classification, Exact Solutions and Conservation Laws of (2+1)-dimensional Time Fractional Konopelchenko-Dubrovsky Equations   Order a copy of this article
    by Jicheng Yu, Yuqiang Feng 
    Abstract: In this paper, Lie symmetry analysis method is applied to the (2+1)-dimensional time fractional Konopelchenko-Dubrovsky equations, which is an important model in physics. We obtained and classified all the Lie symmetries admitted by the equations according to the coefficients. Then we used the obtained group classification to reduce the (2+1)-dimensional fractional partial differential equations with Riemann-Liouville fractional derivative to some (1+1)-dimensional fractional partial differential equations with Erd'{e}lyi-Kober fractional derivative, thereby getting some exact solutions of the reduced equations. In addition, the new conservation theorem and the generalisation of Noether operators are developed to construct the conservation laws for the equations studied.
    Keywords: Lie symmetry analysis; fractional modified Konopelchenko-Dubrovsky equations; Riemann-Liouville fractional derivative; Erd'{e}lyi-Kober fractional derivative; conservation laws.
    DOI: 10.1504/IJDSDE.2025.10067406
     
  • Existence of Positive Solutions for a Fourth-Order Differential Equation with p-Laplacian and Riemann-Stieltjes Integral Boundary Conditions   Order a copy of this article
    by Yingqiu Wang, Dehong Ji 
    Abstract: This paper investigates a problem concerning the positive solutions for a fourth-order differential equation with p-Laplacian and Riemann-Stieltjes integral boundary conditions. Krasnoselskii proposed a theorem in 1960, which has been known as Krasnoselskiis fixed-point theorem. This paper will use this theorem to derive two significant conclusions regarding the problem to be discussed. It is worth noting that, unlike other problems, the equation studied in this paper has a nonlinear term f that includes the first-order derivative of the unknown function.
    Keywords: p-Laplacian; Riemann-Stieljes integral boundary conditions; Cone; Positive solution; Fixed point theorem.
    DOI: 10.1504/IJDSDE.2024.10067781
     

 

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