Existence and multiplicity of positive solutions for a new class of singular higher-order fractional differential equations with Riemann–Stieltjes integral boundary value conditions

In this work, the aim is to discuss a new class of singular nonlinear higher-order fractional boundary value problems involving multiple Riemann–Liouville fractional derivatives. The boundary conditions are constituted by Riemann–Stieltjes integral boundary conditions. The existence and multiplicity of positive solutions are derived via employing the Guo–Krasnosel’skii fixed point theorem. In addition, the main results are demonstrated by some examples to show their validity.

[1]  Fang Wang,et al.  Iterative Analysis of the Unique Positive Solution for a Class of Singular Nonlinear Boundary Value Problems Involving Two Types of Fractional Derivatives with p-Laplacian Operator , 2019, Complex..

[2]  Lishan Liu,et al.  The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems , 2016 .

[3]  I. Podlubny.  Fractional differential equations , 1998 .

[4]  Yonghong Wu,et al.  The spectral analysis for a singular fractional differential equation with a signed measure , 2015, Appl. Math. Comput..

[5]  A. Cabada,et al.  Positive solutions of nonlinear fractional differential equations with integral boundary value conditions , 2012 .

[6]  Yonghong Wu,et al.  Uniqueness of iterative positive solutions for the singular fractional differential equations with integral boundary conditions , 2016 .

[7]  Lishan Liu,et al.  A numerical algorithm for a class of fractional BVPs with p-Laplacian operator and singularity-the convergence and dependence analysis , 2020, Appl. Math. Comput..

[8]  Xiaozhong Yang,et al.  On eigenvalue intervals of higher-order boundary value problems with a sign-changing nonlinear term , 2011, J. Comput. Appl. Math..

[9]  Yonghong Wu,et al.  Iterative unique positive solutions for a new class of nonlinear singular higher order fractional differential equations with mixed-type boundary value conditions , 2019, Journal of Inequalities and Applications.

[10]  Zhongli Wei,et al.  Positive solutions for a class of fractional boundary value problems , 2016 .

[11]  J. Henderson.  Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions , 2015 .

[12]  Bo Yang,et al.  Positive solutions for a fractional boundary value problem , 2016, Appl. Math. Lett..

[13]  D. O’Regan,et al.  Existence and uniqueness of solutions for singular integral equation , 2008 .

[14]  Xingqiu Zhang,et al.  Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter , 2014, Appl. Math. Comput..

[15]  Limin Guo,et al.  Maximal and minimal iterative positive solutions for singular infinite-point p-Laplacian fractional differential equations , 2018, Nonlinear Analysis: Modelling and Control.

[16]  J. Henderson,et al.  Existence of positive solutions for a singular fractional boundary value problem , 2017 .

[17]  Ahmed Alsaedi,et al.  On a coupled system of fractional differential equations with coupled nonlocal and integral boundary conditions , 2016 .

[18]  Xinguang Zhang,et al.  Bifurcation analysis for a singular differential system with two parameters via to topological degree theory , 2017 .

[19]  Lishan Liu,et al.  Existence and uniqueness of positive solutions for singular fractional differential systems with coupled integral boundary conditions , 2017 .

[20]  Lishan Liu,et al.  Positive solutions for a class of fractional 3-point boundary value problems at resonance , 2017 .

[21]  A. Alsaedi,et al.  Existence theorems for semi-linear Caputo fractional differential equations with nonlocal discrete and integral boundary conditions , 2016 .

[22]  W. Ames,et al.  Nonlinear problems in abstract cones , 1988 .

[23]  Yonghong Wu,et al.  Blow-up of solutions for a nonlinear Petrovsky type equation with initial data at arbitrary high energy level , 2019, Boundary Value Problems.

[24]  Yonghong Wu,et al.  Existence and uniqueness of positive solutions for a class of nonlinear fractional differential equations with mixed-type boundary value conditions , 2018, Nonlinear Analysis: Modelling and Control.

[25]  Aleksandar M. Spasic,et al.  Finite-time stability analysis of fractional order time-delay systems: Gronwall's approach , 2009, Math. Comput. Model..

[26]  Yonghong Wu,et al.  Existence and uniqueness of global mild solutions for a class of nonlinear fractional reaction-diffusion equations with delay , 2016, Comput. Math. Appl..

[27]  Lishan Liu,et al.  Existence of positive solutions for singular fractional differential equations with infinite-point boundary conditions , 2016 .

[28]  Ying Wang,et al.  Uniqueness and existence of positive solutions for the fractional integro-differential equation , 2017 .

[29]  Yonghong Wu,et al.  Iterative unique positive solutions for singular p-Laplacian fractional differential equation system with several parameters , 2018 .

[30]  J. Henderson,et al.  Existence of Nonnegative Solutions for a Fractional Integro-Differential Equation , 2017, Results in Mathematics.

[31]  Yonghong Wu,et al.  Existence of positive solutions for singular higher-order fractional differential equations with infinite-point boundary conditions , 2016 .

[32]  Yonghong Wu,et al.  Uniqueness of positive solutions for the singular fractional differential equations involving integral boundary value conditions , 2018, Boundary Value Problems.

[33]  Johnny Henderson,et al.  Systems of Riemann-Liouville fractional equations with multi-point boundary conditions , 2017, Appl. Math. Comput..

[34]  Y. Cho,et al.  Partial Ordering Methods In Nonlinear Problems , 2004 .

[35]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[36]  Yonghong Wu,et al.  Existence of positive solutions for a singular nonlinear fractional differential equation with integral boundary conditions involving fractional derivatives , 2018, Boundary Value Problems.

[37]  Lishan Liu,et al.  Unique iterative positive solutions for a singular p-Laplacian fractional differential equation system with infinite-point boundary conditions , 2019, Boundary Value Problems.

[38]  Lishan Liu,et al.  Positive solutions of singular boundary value problems for systems of nonlinear fourth order differential equations , 2008 .