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When a first-order irreversible exothermic reaction takes place in a continuously stirred tank reactor (CSTR), the plant model relating the reactor and jacket temperatures along with a measurement delay is of second-order unstable type. Such plants are very challenging to control. Hence, this article focuses on developing an optimal fractional order Lyapunov (FOL) based model reference adaptive control (MRAC) scheme. The optimal values of adaptive gain, as well as extra degree of freedom, are obtained using a modified particle swarm optimization (PSO) algorithm. The closed-loop responses and control efforts are compared with that of FOL based MRAC scheme by using an artificial bee colony (ABC) algorithm to optimize adaptive gain and extra degree of freedom. Moreover, the aforementioned optimization methods are also employed to develop respective optimal fractional order Massachusetts institute of …