In this paper, mixed spectral method is applied to solve the fractional fourth order partial integro-differential equations together with weak singularity. Eigenfunctions of the fourth order self-adjoint positive-definite differential operator are used for the discretization of spatial variable and its derivatives. Also, shifted Legendre polynomials are applied to the discretization of time variable. Numerical results are presented for some problems to demonstrate the usefulness and accuracy of this approach. The method is easy to apply and produces very accurate numerical results.

In this paper, we study First order linear fuzzy differential equations with fuzzy coefficient and initial value. We use the generalized differentiability concept and apply the exponent matrix to present the general form of their solutions. Finally, one example is given to illustrate our results.

We expand a new generalization of the two-dimensional differential trans-form method. The new generalization is based on the two-dimensional differ-ential transform method, fractional power series expansions, and conformable fractional derivative. We use the new method for solving a nonlinear con-formable fractional partial differential equation and a system of conformable fractional partial differential equation. Finally, numerical examples are pre-sented to illustrate the preciseness and effectiveness of the new technique.

Prabhakar fractional operator was applied recently for studying the dynamics of complex systems from several branches of sciences and engineering. In this manuscript, we discuss the regularized Prabhakar derivative applied to fractional partial differential equations using the Sumudu homotopy analysis method(PSHAM). Three illustrative examples are investigated to confirm our main results.