Integral inequalities of systems and the estimate for solutions of certain nonlinear two-dimensional fractional differential systems

Abstract

a b s t r a c tThis paper generalizes the results for the constructions of explicit bounds and the qualitative properties for the solutions of certain two-dimensional fractional differential systems established in a recent paper of the authors. The main generalizations come from an elementary inequality and by means of the modification of Medveď's de-singular approach.

Qualitative analysis for solutions of a certain more generalized two-dimensional fractional differential system with Hadamard derivative

“…h Remark 2.1. We note that the estimate given in (2.4) is slightly different from the result obtained in[24, Theorem 2.3].…”

Asymptotic Integration of Some Classes of Fractional Differential Equations

“…In the proof the following lemma (see [16], [26]) is used. Ä ÑÑ 3.3º Let β, γ and p be positive constants such that…”

On the oscillatory behavior of solutions of nonlinear fractional differential equations

“…Oscillation results for fractional differential equations are scarce; some results can be found in [9][10][11][12]14,15]. It seems that there are no such results for fractional differential equations.…”