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A review on Hermite-Hadamard type inequalities connected with a different classes of convexities and fractional differential operators is presented. In the various classes of convexities it includes, classical convex functions, quasi-convex functions, p-convex functions, strongly-m-convex functions, strongly-(θ,m)-convex functions, (s, m)-convex functions, (θ, h- m)-convex functions, strongly (θ, h- m)-convex functions, (h, m)-convex functions of the second type, m-convex functions, h-convex functions, (h,m)-convex functions, relative-convex functions, exponentially (θ, h- m)-convex functions, harmonically h-convex functions and geometric-arithmetically s-convex functions. In the fractional differential operators it includes, Caputo fractional derivative, k-Caputo fractional derivative and Hilfer fractional derivative.

In this paper, we study nonlocal boundary value problems of nonlinear Caputo fractional differential equations supplemented with Erdélyi-Kober type fractional integral boundary conditions. Existence results are obtained by applying the Mönch's fixed point theorem and the technique of measures of noncompactness. An example illustrating the main result is also constructed.

In this paper we study existence and uniqueness of solutions for a coupled system consisting of fractional differential equations of Caputo type, subject to Riemann–Liouville fractional integral boundary conditions. The uniqueness of solutions is established by Banach contraction principle, while the existence of solutions is derived by Leray–Schauder’s alternative. We also study the Hyers–Ulam stability of mentioned system. At the end, examples are also presented which illustrate our results.

In this paper, we study the existence and uniqueness for nonlinear delay fractional differential equations with two orders of Caputo's fractional derivative using the Banach fixed point theorem. Also, we establish the Ulam stability of solutions. Finally, we give an example to illustrate the results.

The aim of this paper is to present new results on the existence of solutions for a class of boundary value problem for fractional order implicit differential equations involving the Caputo fractional derivative. Our results are based on Schauder's fixed point theorem and the Banach contraction principle fixed point theorem.

We study the existence of solutions for fractional differential inclusions of order q∈ (1,2] with four-point integral boundary conditions. We establish Filippov type existence results in the case of nonconvex set-valued maps.

In the present paper, we use generalized differential transform method (GDTM) to derive solutions of some linear and nonlinear space-time fractional Fokker–Planck equations (FPE) in closed form. The space and time fractional derivatives are considered in Caputo sense and the solutions are obtained in terms of Mittag-Leffler functions.

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