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An Introduction to Fractional Differential Equations

Part of the book series: Industrial and Applied Mathematics ((INAMA))

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Abstract

In this chapter, we discuss some applications of fractional differential equations in control theory. The basic problems in control theory such as observability, controllability, and stability are considered for fractional dynamical systems. Observability and controllability of linear systems are studied via Grammian matrix. Sufficient conditions for the controllability of nonlinear fractional dynamical systems are established by means of the fixed point theorem. Stability of linear and nonlinear systems is discussed. Examples are provided to illustrate the theory and few exercises are given.

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Authors and Affiliations

  1. Department of Mathematics, Bharathiar University, Coimbatore, Tamil Nadu, India

    K. Balachandran

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  1. K. Balachandran
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Correspondence to K. Balachandran .

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© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

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Balachandran, K. (2023). Applications. In: An Introduction to Fractional Differential Equations. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-99-6080-4_4

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