In this paper, we propose a new type of fuzzy fractional differential equations under fuzzy Kolwankar- Gangal local fractional derivatives (for short, fuzzy KG-LFD) using fuzzy Riemann-Liouville differentiability. Then, we prove some basic results in this area like, the relation between different types of fuzzy KG-LFD and their r-cut representations, composition of the fuzzy KG-LFD and the fuzzy local fractional integral. Also, an application is provided in details such that the explicit solutions are expressed through Mittag-Leffler function.

In this paper, an iterative method for obtaining the numerical solutions of fractional partialdifferential equations (FPDEs) is introduced. This method is based on the combination of the differentialtransformation method (DTM) with fractional linear multistep methods (FLMM). The proposed methodhas a very low computational cost, with the help of which partial fractional differential equations areconverted into a system of ordinary differential equations. Then the resulting equations are solved with highaccuracy by applying fractional linear multi-step methods such as fractional Euler The series of solutionsobtained in the differential transformation method has a slow convergence speed in large regions. In thisstudy, by combining the mentioned method with linear multi-step methods, this shortcoming is solved.Numerical results show that the obtained solutions. They are in good agreement with the exact solution ofthe fractional differential equation. The obtained results confirm the proven stability and accuracy of themethod.

In this work, we present some useful results of discrete fractional calculus for interval-valued functions. The composition rules for interval fractional operators are introduced, which are used to construct the general form of the solutions to nonlinear interval fractional difference equations. An illustrative example is provided in which the method of recursive iterations is applied to obtain explicit formulas for the solutions of linear interval fractional difference equations.

In this paper the solution of the Volterra integro-differential equations of fractional order is presented. The proposed method consists in constructing the functional series, sum of which determines the function giving the solution of considered problem. We derive conditions under which the solution series, constructed by the method is convergent. Some examples are presented to verify convergence, efficiency and simplicity of the method.

In this paper we propose a method for computing approximations of solution of fuzzy fractional differential equations using fuzzy variational iteration method. Defining a fuzzy fractional derivative, we verify the utility of the method through two illustrative examples.