**Numerical Solution of System of Fractional Differential Equations in Imprecise Environment**

Najeeb Alam Khan, Oyoon Abdul Razzaq, Asmat Ara and Fatima Riaz

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/64150

#### **Abstract**

Fractional calculus and fuzzy calculus theory, mutually, are highly applicable for showing different aspects of dynamics appearing in science. This chapter provides comprehensive discussion of system of fractional differential models in imprecise environment. In addition, presenting a new vast area to investigate numerical solutions of fuzzy fractional differential equations, numerical results of proposed system are carried out by the Grünwald‐Letnikov's fractional derivative. The stability along with truncation error of the Grünwald‐Letnikov's fractional approach is also proved. Moreover, some numerical experiments are performed and effective remarks are concluded on the basis of efficient convergence of the approximated results towards the exact solutions and on the depictions of error bar plots.

**Keywords:** fuzzy‐valued functions, fuzzy differential equations, fractional differential equations, Grünwald‐Letnikov's derivative
