A Lyapunov-Type Inequality for Partial Differential Equation Involving the Mixed Caputo Derivative

Jie Wang and Shuqin Zhang
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Jie Wang: School of Science, China University of Mining and Technology, Beijing 100083, China
Shuqin Zhang: School of Science, China University of Mining and Technology, Beijing 100083, China

Mathematics, 2020, vol. 8, issue 1, 1-11

Abstract: In this work, we derive a Lyapunov-type inequality for a partial differential equation on a rectangular domain with the mixed Caputo derivative subject to Dirichlet-type boundary conditions. The obtained inequality provides a necessary condition for the existence of nontrivial solutions to the considered problem and an example is given to illustrate it. Moreover, we present some applications to demonstrate the effectiveness of the new results.

Keywords: Lyapunov-type inequality; mixed Riemann–Liouville integral; mixed Caputo derivative; Green’s function; boundary value problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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