Existence of Three Positive Solutions for a Class of Boundary Value Problems of Caputo Fractional q-Difference Equation

Abstract

A class of boundary value problems of Caputo fractional q-difference equation is introduced. Green’s function and its properties for this problem are deduced. By applying these properties and the Leggett-Williams fixed-point theorem, existence criteria of three positive solutions are obtained. At last, some examples are given to illustrate the validity of our main results.

Presence and diversity of positive solutions for a Caputo-type fractional order nonlinear differential equation with an advanced argument

“…During the last few decades diversity of positive solutions of different BVPs for fractional order nonlinear differential equation (FONLDE for short) has extensively considered by using various techniques, for instance see the articles of Agarwal et al [2,3], Afshari et al [1], Asaduzzaman and Ali [5], Bai [8], Chen et al [12], Cu et al [13], Devi et al [17], Sun et al [34], and Torres [36] as well as for lower and upper solutions to the integro-differential and iterative hybrid type fractional differential equations see, Damag et al [14] and Damag et al [15] and for positive solutions of nonlinear dissipative type equations, see Asaduzzaman et al [6].…”