In this paper, the circulatory integral and Routh?s equations of Lagrange systems are established with Riemann-Liouville fractional derivatives, is obtained by making use relationship between integrals derivatives. Thereafter, given based on integral. Two examples presented to illustrate application results.

This study aims to prove some midpoint-type inequalities for fractional extended Riemann–Liouville integrals. Crucial equality is proven build new results. Using this equality, several are established via differentiable convex functions and the proposed operators. To be more specific, well-known Hölder, Jensen, power mean integral employed in demonstrated inequalities. Additionally, many remark...

By constructing an available integral operator and combining Krasnosel’skii-Zabreiko fixed point theorem with properties of Green’s function, this paper shows the existence of multiple positive solutions for a class of m-point second-order Sturm-Liouville-like boundary value problems on time scales with polynomial nonlinearity. The results significantly extend and improve many known results for...

and Dn denotes the derivative operator ∂/∂x1, . . . ,∂xn. The operators in (1.1) provide multidimensional generalizations to the well-known one-dimensional Riemann-Liouville andWeyl fractional integral operators defined in [5] (see also [1]). The paper [7] considers several formulas and interesting properties of (1.1). By invoking the Gauss hypergeometric function 2F1(α,β;γ;x), the following ge...

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