Distributed optimal control problems driven by space-time fractional parabolic equations

Abstract We study distributed optimal control problems, governed by space-time fractional parabolic equations (STFPEs) involving time-fractional Caputo derivatives and spatial of Sturm-Liouville type. first prove existence uniqueness solutions STFPEs on an open bounded interval their regularity. Then we show to a quadratic problem. derive adjoint problem using the right-Caputo derivative in time provide optimality conditions for Moreover, propose finite difference scheme find approximate solution considered In proposed scheme, well-known L1 method has been used derivative, while is approximated Grünwald-Letnikov formula. Finally, demonstrate accuracy performance via examples.