In this study, we introduce conditions for the existence of solutions for an iterative functional differential equation of fractional order. We prove that the solutions of the above class of fractional differential equations are bounded by Tsallis entropy. The method depends on the concept of Hyers-Ulam stability. The arbitrary order is suggested in the sense of Riemann-Liouville calculus.

In this paper, a new class of abstract impulsive Riemann-Liouville fractional partial neutral functional differential equations with infinite delay is introduced. We apply the suitable fixed point theorem together with the Hausdorff measure of noncompactness to investigate the existence of mild solutions for these equations in Banach spaces. Finally, two examples to illustrate the applications ...

In this paper we consider the integral equation of fractional order in sense of Riemann-Liouville operator u(t) = a(t)I[b(t)u(t)] + f(t) with m ≥ 1, t ∈ [0, T ], T < ∞ and 0 < α < 1. We discuss the existence, uniqueness, maximal, minimal and the upper and lower bounds of the solutions. Also we illustrate our results with examples. Full text

Some Hermite-Hadamard type inequalities for generalized k-fractional integrals (which are also named [Formula: see text]-Riemann-Liouville fractional integrals) are obtained for a fractional integral, and an important identity is established. Also, by using the obtained identity, we get a Hermite-Hadamard type inequality.

In the present work we discuss the existence of solutions for a system of nonlinear fractional integro-differential equations with initial conditions. This system involving the Caputo fractional derivative and Riemann−Liouville fractional integral. Our results are based on a fixed point theorem of Schauder combined with the diagonalization method.

Smoothness and asymptotic behaviors are studied for the densities of the law of the occupation time on the positive line for Bessel bridges and the normalized excursion of strictly stable processes. The key role is played by these properties for functions defined by Riemann–Liouville fractional integrals.

We investigate exact enlarged controllability for time fractional diffusion systems of Riemann–Liouville type. The Hilbert uniqueness method is used to prove exact enlarged controllability for both cases of zone and pointwise actuators. A penalization method is given and the minimum energy control is characterized.

Comparison results of the nonlinear scalar Riemann-Liouville fractional differential equation of order q, 0 < q ≤ 1, are presented without requiring Hölder continuity assumption. Monotone method is developed for finite systems of fractional differential equations of order q, using coupled upper and lower solutions. Existence of minimal and maximal solutions of the nonlinear fractional different...

In this paper, using the identity proved [43]in for fractional integrals, some new Ostrowski type inequalities for Riemann-Liouville fractional integrals of functions of two variables are established. The established results in this paper generalize those results proved in [43].

Let D denote the Riemann-Liouville fractional differential operator of order α. Let 1 < α < 2 and 0 < β < α. Define the operator L by L = D − aD where a ∈ R. We give sufficient conditions for the existence of solutions of the nonlinear fractional boundary value problem Lu(t) + f(t, u(t)) = 0, 0 < t < 1, u(0) = 0, u(1) = 0.