Abstract. In several fields of Physics, Chemistry and Ecology, some models are described by Liouville systems. In this article we first prove a uniqueness result for a Liouville system in R. Then we establish an uniform estimate for bubbling solutions of a locally defined Liouville system near an isolated blowup point. The uniqueness result, as well as the local uniform estimates are crucial in...

In this paper, we propose a numerical method to estimate the unknown order of a Riemann–Liouville fractional derivative for a fractional Stokes’ first problem for a heated generalized second grade fluid. The implicit numerical method is employed to solve the direct problem. For the inverse problem, we first obtain the fractional sensitivity equation by means of the digamma function, and then we...

One of the central problems of mathematics in the second half of the 19th century and at the beginning of the 20th century was the problem of uniformization of Riemann surfaces. The classics, Klein [1] and Poincaré [2], associated it with studying second-order ordinary differential equations with regular singular points. Poincaré proposed another approach to the uniformization problem [3]. It c...

‎in this paper‎, ‎we study stability of fractional-order nonlinear dynamic systems by means of lyapunov‎ ‎method‎. ‎to examine the obtained results‎, ‎we employe the developed techniques on test examples‎.

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

Abstract Inequalities play a major role in pure and applied mathematics. In particular, the inequality plays an important study of Rosseland’s integral for stellar absorption. this paper we obtain new Milne-type inequalities, apply them to generalized Riemann–Liouville-type operators, which include most known Riemann–Liouville operators.

in this paper, the homotopy perturbation method (hpm) is applied to obtain an approximate solution of the fractional bratu-type equations. the convergence of the method is also studied. the fractional derivatives are described in the modi ed riemann-liouville sense. the results show that the proposed method is very ecient and convenient and can readily be applied to a large class of fractional...

In this paper we initiate the oscillation theory for fractional differential equations. Oscillation criteria are obtained for a class of nonlinear fractional differential equations of the form D ax+ f1(t, x) = v(t) + f2(t, x), lim t→a+ J1−q a x(t) = b1, where D a denotes the Riemann-Liouville differential operator of order q, 0 < q ≤ 1. The results are also stated when the Riemann-Liouville dif...

and Applied Analysis 3 Definition 2.2 see 18 . The standard Riemann-Liouville fractional derivative of order α > 0 of a continuous function y : a,∞ → R is given by D a y t 1 Γ n − α ( d dt )n ∫ t a t − s n−α−1y s ds, 2.2 where n α 1, provided that the integral on the right-hand side converges. Definition 2.3 see 18 . The Riemann-Liouville fractional integral of order α > 0 of a function y : a,∞...