Nonlinear Functional Analysis and Applications

The Basic Sciences Research Institute, Kyungnam University (경남대학교 기초과학연구소)
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QUALITATIVE ANALYSIS OF A PROPORTIONAL CAPUTO FRACTIONAL PANTOGRAPH DIFFERENTIAL EQUATION WITH MIXED NONLOCAL CONDITIONS

  • Khaminsou, Bounmy (Department of Mathematics, Faculty of Science, Burapha University) ;
  • Thaiprayoon, Chatthai (Department of Mathematics, Faculty of Science, Burapha University) ;
  • Sudsutad, Weerawat (Department of General Education, Faculty of Science and Health Technology Navamindradhiraj University) ;
  • Jose, Sayooj Aby (Ramanujan Centre for Higher Mathematics, Alagappa University)
  • Received : 2020.10.01
  • Accepted : 2021.02.05
  • Published : 2021.03.15
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Abstract

In this paper, we investigate existence, uniqueness and four different types of Ulam's stability, that is, Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability of the solution for a class of nonlinear fractional Pantograph differential equation in term of a proportional Caputo fractional derivative with mixed nonlocal conditions. We construct sufficient conditions for the existence and uniqueness of solutions by utilizing well-known classical fixed point theorems such as Banach contraction principle, Leray-Schauder nonlinear alternative and $Krasnosel^{\prime}ski{\breve{i}}{^{\prime}}s$ fixed point theorem. Finally, two examples are also given to point out the applicability of our main results.

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References

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