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Analysis of 2-Term Fractional-Order Delay Differential Equations

  • Sachin BhalekarEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

The value of a state variable at past time usually affects its rate of change at the present time. So, it is very natural to consider the delay while modeling the real-life systems. Further, the nonlocal fractional derivative operator is also useful in modeling memory in the system. Hence, the models involving delay as well as fractional derivative are very important. In this chapter, we review the basic results regarding the dynamical systems, fractional calculus, and delay differential equations. Further, we analyze 2-term nonlinear fractional-order delay differential equation \(D^\alpha x + c D^\beta x = f\left( x,x_\tau \right) \), with constant delay \(\tau >0\) and fractional orders \(0<\alpha<\beta <1\). We present a numerical method for solving such equations and present an example exhibiting chaotic oscillations.

Notes

Acknowledgements

The author acknowledges the Council of Scientific and Industrial Research, New Delhi, India for funding through Research Project [25(0245)/15/EMR-II] and the Science and Engineering Research Board (SERB), New Delhi, India for the Research Grant [Ref. MTR/2017/000068] under Mathematical Research Impact Centric Support (MATRICS) Scheme.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsShivaji UniversityVidyanagar, KolhapurIndia

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