A NEW FRACTIONAL BOUNDARY VALUE PROBLEM AND LYAPUNOV-TYPE 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.

Automated summary

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.