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A survey of results on Lyapunov-type inequalities for fractional differential equations associated with a variety of boundary conditions is presented. We have included some recent work on the topic dealing with sequential, Caputo-Fabrizio, Hadamard, Hilfer, Katugampola, hyprid, or nested fractional derivatives. We have also focused on Lyapunov-type inequalities for problems containing fractional derivatives with respect to a certain function, systems of fractional differential equations, and conformable derivatives. Furthermore, Lyapunov-type inequalities for fractional differential equations based on non Green function approach are discussed.

In this paper, we derive several subordination results for a certain class of analytic functions defined by the generalized Al-Oboudi differential operator. Relevant connections of some of the results obtained with those in earlier works are also provided.

In this paper, we establish the existence and uniqueness of solution for a class of initial value problem for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, Schauder' fixed point theorem and the nonlinear alternative of Leray-Schauder type. As applications, two examples are included to show the applicability of our results.

In this paper, we improve and further generalize some Ostrowski-Grüss type inequalities for the fractional integrals by using new Montogomery identities.

In this paper, we shall establish sufficient conditions for the existence of solutions for a first order boundary value problem for fractional differential equations.