Abstract
In this article, we study the controllability of dynamical systems with \((k,\psi )\)-Hilfer fractional derivative. The Gramian matrix is used to get a necessary and sufficient controllability requirement for linear systems, which are characterized by the Mittag–Leffler (M–L) functions, while the fixed point approach is used to arrive at adequate controllability criteria for nonlinear systems. The novel feature of this study is to inquire into the controllability notion by using \((k,\psi )\)-Hilfer fractional derivative, the most generalized variant of the Hilfer derivative. The advantage of this type of fractional derivative is that it recovers the majority of earlier studies on fractional differential equations (FDEs). Finally, we provide numerical examples to illustrate our main results.
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Acknowledgements
Authors are grateful to the learned referee for the useful comments and suggestions which have led us to improve the quality of the article. The first author thanks to University Grant Commission, India for the support of Maulana Azad National Fellowship under Grant No. 201920- 413816.
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Haque, I., Ali, J. & Malik, M. Controllability of fractional dynamical systems with \((k,\psi )\)-Hilfer fractional derivative. J. Appl. Math. Comput. (2024). https://doi.org/10.1007/s12190-024-02078-4
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DOI: https://doi.org/10.1007/s12190-024-02078-4
Keywords
- Fractional dynamical systems
- \((k,\psi )\)-Hilfer
- M–L functions
- Controllability
- Gramian matrix
- Fixed point theorem