The unique iterative positive solution of fractional boundary value problem with q-difference

Abstract In this work, we mainly improve the results in Wang (2018). For a fractional q-difference Schrodinger equation, the authors of Wang (2018) obtain twin positive solutions, which maybe identical. We deal with a more general form of fractional q-difference Schrodinger equation whose nonlinear term has two space variables and can be singular with respect to the second space variable. Only by the iterative algorithm, we obtain the unique positive solution. The main results in Wang (2018) have been proved to be a particular corollary of our work. An example is also given to illustrate the results.

[1]  Zengqin Zhao,et al.  Existence and uniqueness of symmetric positive solutions of 2n2n-order nonlinear singular boundary value problems , 2013, Appl. Math. Lett..

[2]  Lingju Kong,et al.  Existence of positive solutions to a higher order singular boundary value problem with fractional q-derivatives , 2013 .

[3]  Lishan Liu,et al.  Existence and uniqueness of iterative positive solutions for singular Hammerstein integral equations , 2017 .

[4]  J. Mao,et al.  The existence and uniqueness of positive solutions for integral boundary value problems , 2009 .

[5]  Christopher S. Goodrich,et al.  Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions , 2011, Comput. Math. Appl..

[6]  Ahmed Alsaedi,et al.  Existence of solutions for nonlinear fractional q-difference integral equations with two fractional orders and nonlocal four-point boundary conditions , 2014, J. Frankl. Inst..

[7]  Ricardo Almeida,et al.  Existence results for fractional q-difference equations of order α∈]2, 3[ with three-point boundary conditions , 2014, Commun. Nonlinear Sci. Numer. Simul..

[8]  Ravi P. Agarwal,et al.  Certain fractional q-integrals and q-derivatives , 1969, Mathematical Proceedings of the Cambridge Philosophical Society.

[9]  J. Mao,et al.  The Unique Positive Solution for Singular Hadamard Fractional Boundary Value Problems , 2019, Journal of Function Spaces.

[10]  Aixia Qian,et al.  Laplace’s equation with concave and convex boundary nonlinearities on an exterior region , 2017, Boundary Value Problems.

[11]  Guotao Wang,et al.  Twin iterative positive solutions of fractional -difference Schrödinger equations , 2018, Appl. Math. Lett..

[12]  Zengqin Zhao,et al.  On existence and uniqueness of positive solutions for integral boundary boundary value problems , 2010 .

[13]  Yonghong Wu,et al.  The uniqueness of positive solution for a fractional order model of turbulent flow in a porous medium , 2014, Appl. Math. Lett..

[14]  Rui A. C. Ferreira,et al.  Positive solutions for a class of boundary value problems with fractional q-differences , 2011, Comput. Math. Appl..

[15]  Zengqin Zhao,et al.  The Exact Iterative Solution of Fractional Differential Equation with Nonlocal Boundary Value Conditions , 2018, Journal of Function Spaces.