期刊
JOURNAL OF MATHEMATICAL INEQUALITIES
卷 15, 期 1, 页码 81-93出版社
ELEMENT
DOI: 10.7153/jmi-2021-15-08
关键词
Lyapunov's inequality; fractional derivative; Green's function; Mittag-Leffler function
In this paper, a new modified version of fractional boundary value problem (BVP) has been studied. A Lyapunov-type inequality for the BVP subject to Dirichlet-type boundary conditions is obtained using the vector Green function. Furthermore, a criteria for the nonexistence of real zeros of certain Mittag-Leffler functions is inferred using the generalized Wright functions based on the new inequality.
Throughout this paper, we study a new modified version of fractional boundary value problem (BVP) of the form ((C)(a)D(alpha)y)(t) + p(t)y'(t) + q(t)y(t)= 0, a < t < b, 2 < alpha <= 3, with y(a) = y'(a) =y(b) = 0, where p is an element of C-1 ([a,b]) and q is an element of C([a,b]). Using the vector Green function we obtain a Lyapunov-type inequality for the BVP subject to Dirichlet-type boundary conditions. Moreover, we utilize the new inequality to infer a criteria for the nonexistence of real zeros of some certain Mittag-Leffler functions using the generalized Wright functions.
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