Summary: Autoimmune diseases are generated through irregular immune response of the human body. Psoriasis is one type of autoimmune chronic skin diseases that is differentiated by T-cells mediated hyper-proliferation of epidermal keratinocytes. Dendritic cells and CD8\(^{+}\) T-cells have a significant role for the occurrence of this disease. In this paper, the authors have developed a mathematical model of psoriasis involving CD4\(^{+}\) T-cells, dendritic cells, CD8\(^{+}\) T-cells and keratinocyte cell populations using the fractional differential equations with the effect of cytokine release to observe the impact of memory on the cell-biological system. Using fractional calculus, the authors try to explore the suppressed memory, associated with the cell-biological system and to locate the position of keratinocyte cell population as fractional derivative possess non-local property. Thus, the dynamics of psoriasis can be predicted in a better way using fractional differential equations rather than its corresponding integer order model. Finally, the authors introduce drug into the system to obstruct the interaction between CD4\(^{+}\) T-cells and keratinocytes to restrict the disease psoriasis. The authors derive the Euler-Lagrange conditions for the optimality of the drug induced system. Numerical simulations are made through Matlab by developing iterative schemes.