Solvability of Some Fractional Boundary Value Problems with a Convection Term

Abstract

This paper is devoted to the research of some Caputo’s fractional derivative boundary value problems with a convection term. By the use of some fixed-point theorems and the properties of Green function, the existence results of at least one or triple positive solutions are presented. Finally, two examples are given to illustrate the main results.

On solutions of a class of three-point fractional boundary value problems

“…An extensive literature related to the existence of solutions of boundary value problems for fractional differential equations addressed by the use of various nonlinear functional analysis method. For example, fixed point theory [5, 7, 9-11, 19, 21, 25-28, 32, 33, 39, 50, 52, 56], the Mawhin continuation method [3,6,54,57], the Green function method [5,44,45], the integral operator method [4,8,13,14,17,22,30,31,35,36,38,49,51,53], the upper and lower solution method [12,15,18,29], the numerical method [40-43, 46, 55], and the technique of barrier strips [4,16,20,24,34,37].…”

Positive solutions for a boundary value problem of fractional differential equation with p-Laplacian operator

“…In consequence, fractional differential equations have been of great interest. For details, see fractional two-point boundary value problems [29,31,32,35,57,64], fractional boundary value problems at resonance [5,8,67,69,71], fractional multi-point problems with nonresonance [5,8,44,48,58,61,68], fractional initial value problems [6,7,34], fractional impulsive problems [48,72], fractional integral boundary value problems [14,40,46,62], fractional p-Laplace problems [15, 18, 20-22, 28, 36, 39, 45, 47, 49, 50, 52, 60, 65, 66, 70], fractional problems with lower and upper solution [7,39,51,59], fractional control problems, [41,43,[53][54][55][56], fractional soliton problems [19,24,26,42], fractional singular problems [17,27,30,37,…”

Existence and uniqueness of solutions for mixed fractional q-difference boundary value problems

“…In 2011, Zhao and Sun et al [10] In 2011, Feng and Sun et al [11] discussed the boundary value problem to the following system of fractional differential equations: For more information about boundary value problems of fractional differential equations; see [12][13][14][15].…”