Necessary optimality conditions for ψ-Caputo fractional optimal control problems

This paper presents a comprehensive investigation into fractional-order optimal control problems using the ψ -Caputo derivative. Building upon the fundamental concepts of optimal control theory, we formulate a generalized model incorporating fractional-order dynamics. The study derives necessary and sufficient optimality conditions, establishes the equivalence between these conditions under certain assumptions, and proposes an numerical algorithm for solving the resulting fractional differential equations. This approach transforms the complex fractional-order problem into a set of algebraic equations solvable via standard computational methods. The efficacy of the proposed methodology is demonstrated through a comparative analysis of numerical results obtained using various scaling functions ψ . This work constitutes the first systematic exploration of ψ -Caputo fractional-order optimal control problems, offering valuable insights into the application of advanced fractional calculus techniques in modern control systems design and optimization.