On the existence of positive solutions for generalized fractional boundary value problems. (English) Zbl 1513.34116
Summary: The existence of positive solutions is established for boundary value problems defined within generalized Riemann-Liouville and Caputo fractional operators. Our approach is based on utilizing the technique of fixed point theorems. For the sake of converting the proposed problems into integral equations, we construct Green functions and study their properties for three different types of boundary value problems. Examples are presented to demonstrate the validity of theoretical findings.
MSC:
| 34B18 | Positive solutions to nonlinear boundary value problems for ordinary differential equations |
| 34A08 | Fractional ordinary differential equations |
| 26A33 | Fractional derivatives and integrals |
| 34B27 | Green’s functions for ordinary differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
Keywords:
generalized fractional differential equations \(\psi\)-Riemann-Liouville; existence of positive solutions; fixed point theorems; fractional derivative; \(\psi\)-Caputo fractional derivativeReferences:
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