Generalized conformable variational calculus and optimal control problems with variable terminal conditions

Beyza Billur İskender Eroǧlu; Dilara Yapışkan; Beyza Billur İskender Eroǧlu; Dilara Yapışkan

doi:10.3934/math.2020077

AIMS Mathematics

2020, Volume 5, Issue 2: 1105-1126. doi: 10.3934/math.2020077

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Research article Special Issues

Generalized conformable variational calculus and optimal control problems with variable terminal conditions

Department of Mathematics, Balıkesir University, Balıkesir, 10145, Turkey

Received: 23 October 2019 Accepted: 08 December 2019 Published: 13 January 2020
MSC : 34H05, 49K15

This paper provides generalized transversality conditions for the problems of variational calculus and optimal control, constructed by the conformable derivative. The generalized term is used to emphasize the problems with performance indexes containing the conformable derivative and defined by the classical integral and to distinguish them from the problems with performance indexes defined by the conformable integral. Special cases of the generalized transversality conditions both for variational calculus and optimal control are exhibited and supported by illustrative examples.
- conformable derivative,
- fractional order,
- optimal control,
- variational calculus,
- generalized Euler-Lagrange equation,
- generalized transversality condition
Citation: Beyza Billur İskender Eroǧlu, Dilara Yapışkan. Generalized conformable variational calculus and optimal control problems with variable terminal conditions[J]. AIMS Mathematics, 2020, 5(2): 1105-1126. doi: 10.3934/math.2020077

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Abstract

This paper provides generalized transversality conditions for the problems of variational calculus and optimal control, constructed by the conformable derivative. The generalized term is used to emphasize the problems with performance indexes containing the conformable derivative and defined by the classical integral and to distinguish them from the problems with performance indexes defined by the conformable integral. Special cases of the generalized transversality conditions both for variational calculus and optimal control are exhibited and supported by illustrative examples.

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