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Stability of Integral Caputo-Type Boundary Value Problem with Noninstantaneous Impulses

  • Akbar ZadaEmail author
  • Sartaj Ali
Original Paper
  • 2 Downloads

Abstract

The modeling of a natural phenomena give soar to impulsive (instantaneous and noninstantaneous) fractional Caputo differential equations with boundary conditions. The behavior of the natural real world phenomena can be observed from the solutions of corresponding impulsive fractional Caputo differential equations with boundary conditions. Therefore, the existence, uniqueness and Ulam’s stability of the solutions of impulsive fractional Caputo differential equations are the most important concepts in fractional calculus. In this article, we take a noninstantaneous impulsive fractional Caputo differential equations with integral boundary conditions. The main objective of this article is, to study the existence, uniqueness and different types of Ulam’s stability for the solutions of fractional Caputo differential equations with noninstantaneous impulses and integral boundary conditions. At last, few examples are given to illustrate the new work.

Keywords

Caputo fractional derivative Riemann–Liouville fractional integral Impulses Ulam–Hyers–Rassias stability Fixed point theorem 

Mathematics Subject Classification

34A08 34B27 

Notes

Acknowledgements

The authors express their sincere gratitude to the Editor and referees for the careful reading of the original manuscript and useful comments that helped to improve the presentation of the results.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Nature India Private Limited 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of PeshawarPeshawarPakistan

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