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Duality Results for Fractional Variational Problems and Its Application

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Abstract

This article is tendered to discuss the nondifferentiable class of multiobjective variational problems of minimizing a vector of quotients of functionals of curvilinear integral type with cone constraints, and duality theorems are proved under assumptions of higher-order \((F,\alpha ,\rho ,d)\)-pseudoconvexity. The value of the objective function of primal cannot exceed the value of dual is shown by giving the weak duality theorem. Moreover, we study the connection between the values of the primal problem and dual problem in strong and converse duality theorems. Also, we have obtained the examples of functionals which are higher-order \((F,\alpha ,\rho ,d)\)-pseudoconvex but not higher-order F-pseudoconvex and not \((F,\alpha ,\rho ,d)\)-pseudoconvex. We have given a real-world application verifying the weak duality theorem.

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Acknowledgements

The authors are grateful to the editor and reviewers for their valuable comments and suggestions. The first author is grateful to CSIR, New Delhi, India for providing (File 09/677(0043)/2019-EMR-I) financial support for this research work and the second author gratefully acknowledges technical support from the Seed Money Project TU/DORSP/57/7293 of TIET, Patiala. Also, authors acknowledge DST-FIST (Govt. of India, SR/FST/MS-1/2017/13) for sponsoring School of Mathematics, TIET, Patiala.

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  1. School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, 147 004, India

    Vivek Dhingra & N. Kailey

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  1. Vivek Dhingra
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  2. N. Kailey
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Correspondence to N. Kailey.

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Communicated by Anton Abdulbasah Kamil.

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Dhingra, V., Kailey, N. Duality Results for Fractional Variational Problems and Its Application. Bull. Malays. Math. Sci. Soc. 45, 2195–2223 (2022). https://doi.org/10.1007/s40840-022-01324-x

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  • DOI: https://doi.org/10.1007/s40840-022-01324-x

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