In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

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, we investigate the solutions of a class of-Hilfer fractional differential equations with the initial values in the sense of-fractional integral by using the successive approximation techniques. Next, the continuous dependence of a solution for the given Cauchy-type problem is presented.

In this paper, we apply fractional complex transform to convert the fractional nonlinear Schrodinger equations to the nonlinear Schrodinger equations.

In this paper we propose a method for computing approximations of solution of fractional differential equations using Legendre polynomials and Adomian decomposition method.

In this study, we construct the fractional-order Bernstein wavelets for solving stochastic fractional integro-differential equations. Fractional-order Bernstein wavelets and their properties are presented for the first time.  The fractional integral operator of fractional-order Bernstein wavelets together with the Gaussian integration method is applied to reduce stochastic fractional integro-differential equations to the solution of algebraic equations which can be simply solved to obtain the solution of the problem.  Also, an error estimation for our approach is introduced.  The numerical results demonstrate that our scheme is simply applicable, efficient, powerful and very precise at the small number of basis functions.

To solve fractional-order differential equations (FODEs) with Antagana-Baleanu fractional operator (ABFO), an efficient strategy based on variational iteration method (VIM) and natural transform(NT) is given. Natural variational iteration technique is the name of this method (NVIM). This work also investigates the convergence of the solution of general FODEs obtained by the suggested method given the theory of fixed point and Banach spaces. Furthermore, the error analysis of the NVIM solution is also discussed. Two problems are solved to validate and efficacy demonstrate the of the present. It is also demonstrated that the results obtained from the suggested technique are in excellent agreement with the exact solution. The NVIMs numerical results reveal that the technique is simple to implement and computationally appealing.