An inventory model for partial backlogging items with memory effect

Inventory control is considered one of the most widely documented topics in reality. Fractional derivatives and integration part fractional calculus. calculus generalized ordinary The memory physical phenomena a highly concerning topic but it neglected with describing terms integer-order differential equation. To discuss inventory model, derivative tools are considered. A at any point gives previous marginal output current for input. In this shortage considered, during period, demand partially backlogged. Depending on low partial backlogging rate high rate, result effect varies total average cost optimal ordering interval. Moreover, order to show relationship between models classical two types indices have been considered: (i) index (ii) integral index. For certain effect, minimized same rate.