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This chapter explores second-order differential equations that involve delays and random effects, focusing on how these equations can be solved by including random operators. The Schauder fixed-point theorem is employed to demonstrate the existence of solutions to these equations. The chapter also explains how the system can be controlled under certain conditions. To make the ideas clear, an example is included to show how the theory can be applied in real situations where there are delays and randomness.

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Existence and Controllability for Second-Order Neutral Functional Integro-differential Equations with Infinite Delay and Random Effects

  • 章节

  • 发表日期：

    2025年

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  • Gunasekar Tharmalingam,
  • Madhumitha Srinivasan,
  • Shyam Sundar Santra,
  • Dumitru Baleanu

摘要

This chapter explores second-order differential equations that involve delays and random effects, focusing on how these equations can be solved by including random operators. The Schauder fixed-point theorem is employed to demonstrate the existence of solutions to these equations. The chapter also explains how the system can be controlled under certain conditions. To make the ideas clear, an example is included to show how the theory can be applied in real situations where there are delays and randomness.