Abstract
In this paper, we study a class of fractional q-difference equations with nonhomogeneous boundary conditions. By applying the classical tools from functional analysis, sufficient conditions for the existence of single and multiple positive solutions to the boundary value problem are obtained in term of the explicit intervals for the nonhomogeneous term. In addition, some examples to illustrate our results are given.MSC:34A08, 34B18, 39A13.
Highlights
Fractional differential equations have attracted considerable interest because of its demonstrated applications in various fields of science and engineering including fluid flow, rheology, diffusive transport akin to diffusion, electrical networks, probability [, ]
Many researchers have studied the existence of solutions to fractional boundary value problems; for example, see [ – ] and the references therein
The early work on q-difference calculus or quantum calculus dates back to Jackson’s papers [ ], basic definitions and properties of quantum calculus can be found in the book [ ]
Summary
Fractional differential equations have attracted considerable interest because of its demonstrated applications in various fields of science and engineering including fluid flow, rheology, diffusive transport akin to diffusion, electrical networks, probability [ , ]. Many researchers have studied the existence of solutions (or positive solutions) to fractional boundary value problems; for example, see [ – ] and the references therein. The study of boundary value problems for nonlinear fractional q-difference equations is still in the initial stage and many aspects of this topic need to be explored.
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