The existence of solutions for nonlinear fractional boundary value problem and its Lyapunov-type inequality involving conformable variable-order derivative

Abstract

We consider a nonlinear fractional boundary value problem involving conformable variable-order derivative with Dirichlet conditions. We prove the existence of solutions to the considered problem by using the upper and lower solutions' method with Schauder's fixed-point theorem. In addition, under some assumptions on the nonlinear term, a new Lyapunov-type inequality is given for the corresponding boundary value problem. The obtained inequality provides a necessary condition for the existence of nontrivial solutions to the considered problem and a method to prove uniqueness for the nonhomogeneous boundary value problem. These new results are illustrated through examples.

Artificial Neural Network Technique for Solving Variable Order Fractional Integro-Differential Algebraic Equations

“…In this section, we recall some definitions and general concepts related to fractional calculus which may be used further in this paper [38][39][40][41]. Let α: [a,∞) → (0, 1] and 𝐶𝐷 𝑎 𝛼(𝑡) denotes the conformable fractional derivative.…”

Analysis of a novel coronavirus (2019-nCOV) system with variable Caputo-Fabrizio fractional order

“…Vital physical, real-world problems phenomena are well presented by FDEs, namely, acoustics, viscoelasticity, electrochemistry, electromagnetics, material science. The Complex system is describing by FC due to its applications [1] , [2] , [3] , [4] , [5] , [23] , [24] , [25] .…”