| Issue |
RAIRO-Oper. Res.
Volume 56, Number 2, March-April 2022
|
|
|---|---|---|
| Page(s) | 637 - 648 | |
| DOI | https://doi.org/10.1051/ro/2022035 | |
| Published online | 14 April 2022 | |
Sufficient conditions for extremum of fractional variational problems
1
Department of Mathematics, Veer Surendra Sai University of Technology, Burla 768018, India
2
Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA
* Corresponding author: skpadhan_math@vssut.ac.in
Received:
31
July
2021
Accepted:
27
February
2022
Sufficient conditions for extremum of fractional variational problems are formulated with the help of Caputo fractional derivatives. The Euler–Lagrange equation is defined in the Caputo sense and Jacobi conditions are derived using this. Again, Wierstrass integral for the considered functional is obtained from the Jacobi conditions and the transversality conditions. Further, using the Taylor’s series expansion with Caputo fractional derivatives in the Wierstrass integral, the Legendre’s sufficient condition for extremum of the fractional variational problem is established. Finally, a suitable counterexample is presented to justify the efficacy of the fresh findings.
Mathematics Subject Classification: 26A33 / 58E15 / 34K37 / 49K10 / 49K20 / 35R11
Key words: Caputo fractional derivative / Jacobi conditions / transversality conditions / Wierstrass integral / Legendre’s condition
© The authors. Published by EDP Sciences, ROADEF, SMAI 2022
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