In this paper, we , nd an integral representation for the fundamental solution of the Fractional Ostrovsky Equation in terms of the Airy and Bessel-Wright functions. The Equation is studied in the sense of the Weyl Fractional derivative and the solu-tion is presented as the Airy transforms of Wright functions. Using the asymptotic expansion of Wright function the asymptotic behavior of solution is also discussed.

In this study, we give results on the existence and uniqueness of solutions for generalized Fractional integrodifferential Equations with a nonlocal terminal condition. We have proved the existence of solutions to the problem proposed using the Schauder fixed point theorem and the uniqueness of its solutions is proved using the Banach fixed point theorem. At the end, we discussed the examples to support our results.

In this article, we study a new nonlinear Langevin Equation of two Fractional orders with Fractional boundary value conditions which is a generalization of previous Langevin Equations. Based on Banach and Schauder fixed point theorems, the existence and uniqueness of solutions of this Equation are investigated. Moreover, our hypotheses are simpler than similar works.

Recently Fractional cable Equation has been investigated by many authors who have applied it in various areas. Here we introduce and investigate a generalized space-time Fractional cable Equation associated with Riemann-Liouville and Hilfer Fractional derivatives. By mainly applying both Laplace and Fourier transforms, we express the solution of the proposed generalized Fractional cable Equation as H-functions. The main results here are general enough to be specialized to yield many new and known results, only several of which are demonstrated in corollaries. Finally, we consider the moment of the Green function with its several asymptotic formulas.

Fuzzy Fractional heat Equations (FFHEs) are utilized to an-alyze the behaviour of the certain phenomena in various mathematical and scienti, c models. The main goal of this paper is to construct the solution of fuzzy Fractional heat Equations by taking a reliable recipe of Sumudu transformation method and homotopy analysis method into account. These method allow us to remove the di, culties and restric-tions confronted in other methods. The feasibility of this method is con, rmed by given numerical examples. The result presented that the proposed method is suitable, powerful and reliable for obtaining the solution of fuzzy Fractional problems with FFHEs.