Iterative unique positive solutions for a new class of nonlinear singular higher order fractional differential equations with mixed-type boundary value conditions. (English) Zbl 1499.34085
Summary: In this paper, we consider a new class of singular nonlinear higher order fractional boundary value problems supplemented with sum of Riemann-Stieltjes integral type and nonlocal infinite-point discrete type boundary conditions. The fractional derivative of different orders is involved in the nonlinear terms and boundary conditions, and the nonlinear terms are allowed to be singular in regard to not only time variable but also space variables. A unique positive solution is established by using the fixed point theorem of mixed monotone operator. In addition, some significant properties of the unique solution depending on the parameter \(\lambda\) are stated. In the end, two examples are worked out to illustrate our main results.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 26A33 | Fractional derivatives and integrals |
| 34B18 | Positive solutions to nonlinear boundary value problems for ordinary differential equations |
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
Keywords:
fractional differential equations; Riemann-Stieltjes integral; nonlocal infinite-point discrete boundary conditions; uniqueness of solutionsReferences:
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