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A class of piecewise fractional functional differential equations with impulsive

  • Mei Jia EMAIL logo , Tingle Li and Xiping Liu EMAIL logo
Published/Copyright: November 1, 2022
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International Journal of Nonlinear Sciences and Numerical Simulation
From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 24 Issue 5

Abstract

In this paper, we study a class of piecewise fractional functional differential equations with impulsive and integral boundary conditions. By using Schauder fixed point theorem and contraction mapping principle, the results for existence and uniqueness of solutions for the piecewise fractional functional differential equations are established. And by using cone stretching and cone contraction fixed point theorems in norm form, the existence of positive solutions for the equations are also obtained. Finally, an example is given to illustrate the effectiveness of the conclusion.

Keywords: boundary value problems; fixed point theorems; impulses; piecewise fractional functional differential equations; positive solutions; the existence and uniqueness of solutions
MSC: 34A08; 34B10; 34K37
Corresponding authors: Mei Jia and Xiping Liu, College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China, E-mail: (M. Jia) and (X. Liu)

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 11171220

Acknowledgments

The authors would like to thank the editor, advisory editor and the anonymous referees for their contributions to this article and their valuable suggestions for improving this article.

  1. Author contributions: The authors declare that the study was realized in collaboration with equal responsibility. All authors read and approved the final manuscript.

  2. Research funding: This work is supported by the National Natural Science Foundation of China (Grant No. 11171220).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2021-07-27
Accepted: 2022-09-18
Published Online: 2022-11-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/ijnsns-2021-0306
Keywords for this article
boundary value problems; fixed point theorems; impulses; piecewise fractional functional differential equations; positive solutions; the existence and uniqueness of solutions

Articles in the same Issue

  1. Frontmatter
  2. Original Research Article
  3. Hybrid solitary wave solutions of the Camassa–Holm equation
  4. Numerical simulations of wave propagation in a stochastic partial differential equation model for tumor–immune interactions
  5. A Chebyshev collocation method for solving the non-linear variable-order fractional Bagley–Torvik differential equation
  6. Higher order codimension bifurcations in a discrete-time toxic-phytoplankton–zooplankton model with Allee effect
  7. Numerical modeling of the dam-break flood over natural rivers on movable beds
  8. A class of piecewise fractional functional differential equations with impulsive
  9. Lie symmetry analysis for two-phase flow with mass transfer
  10. Asymptotic behavior for stochastic plate equations with memory in unbounded domains
  11. Discussion on controllability of non-densely defined Hilfer fractional neutral differential equations with finite delay
  12. A linearized finite difference scheme for time–space fractional nonlinear diffusion-wave equations with initial singularity
  13. Ground state solutions of Schrödinger system with fractional p-Laplacian
  14. Bifurcation analysis of a new stochastic traffic flow model
  15. An uncertainty measure based on Pearson correlation as well as a multiscale generalized Shannon-based entropy with financial market applications
  16. Hilfer fractional stochastic evolution equations on infinite interval
  17. Iterative learning control for conformable stochastic impulsive differential systems with randomly varying trial lengths
  18. Chebyshev wavelet-Picard technique for solving fractional nonlinear differential equations
  19. Theoretical assessment of the impact of awareness programs on cholera transmission dynamic
  20. Theoretical and numerical analysis of a prey–predator model (3-species) in the frame of generalized Mittag-Leffler law
  21. Controllability discussion for fractional stochastic Volterra–Fredholm integro-differential systems of order 1 < r < 2
  22. Shehu transform on time-fractional Schrödinger equations – an analytical approach
  23. A (2 + 1)-dimensional variable-coefficients extension of the Date–Jimbo–Kashiwara–Miwa equation: Lie symmetry analysis, optimal system and exact solutions
  24. Mathematical model of fluid flow in a double constricted tapered tube with permeable boundary
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