In any business memory effect has great importance in inventory management as memory or past history cannot be ignored from the practical life of the inventory system. Many exogenous inventory parameters and factors at a given time depends not only their current values but also on the past histories. Thus an inventory management is a non Markovian process which can be tackled with memory dependent kernel of fractional derivatives. Another important factor of inventory management is deterioration of items which is directly related with memory effect as long memory of high rate of deterioration leads to poor impact on the business. Effect of long memory on deterioration of items have been studied in this paper using memory kernel of fractional derivatives. Fractional integration has been used to derive fractional order holding cost, deterioration cost, shortage cost and opportunity cost. Our analysis shows that for gradually increasing memory effect profit gradually increases. Our model is developed as a memory dependent inventory model. ©2021 L&H Scientific Publishing, LLC. All rights reserved.