Analysis of some Katugampola fractional differential equations with fractional boundary conditions

Barbara Łupińska; Ewa Schmeidel; Barbara Łupińska; Ewa Schmeidel

doi:10.3934/mbe.2021359

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 6: 7269-7279. doi: 10.3934/mbe.2021359

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Analysis of some Katugampola fractional differential equations with fractional boundary conditions

Barbara Łupińska ,
Ewa Schmeidel ^,

Institute of Computer Science, University of Bialystok, Konstantego Ciołkowskiego 1M, 15-245 Białystok, Poland

Received: 23 July 2021 Accepted: 10 August 2021 Published: 27 August 2021

In this work, some class of the fractional differential equations under fractional boundary conditions with the Katugampola derivative is considered. By proving the Lyapunov-type inequality, there are deduced the conditions for existence, and non-existence of the solutions to the considered boundary problem. Moreover, we present some examples to demonstrate the effectiveness and applications of the new results.
- fractional calculus,
- Lyapunov inequality,
- Green function,
- fractional differential equations,
- Katugampola derivative,
- eigenvalue of fractional differential equation
Citation: Barbara Łupińska, Ewa Schmeidel. Analysis of some Katugampola fractional differential equations with fractional boundary conditions[J]. Mathematical Biosciences and Engineering, 2021, 18(6): 7269-7279. doi: 10.3934/mbe.2021359

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Abstract

In this work, some class of the fractional differential equations under fractional boundary conditions with the Katugampola derivative is considered. By proving the Lyapunov-type inequality, there are deduced the conditions for existence, and non-existence of the solutions to the considered boundary problem. Moreover, we present some examples to demonstrate the effectiveness and applications of the new results.

References

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