On Caputo tempered implicit fractional differential equations in \(b\)-metric spaces. (English) Zbl 1517.34009
Summary: This paper deals with the existence and uniqueness results for a class of problems for nonlinear Caputo tempered implicit fractional differential equations in \(b\)-metric spaces with initial and nonlocal conditions. The arguments are based on some fixed point theorems. Furthermore, two illustrations are presented to demonstrate the plausibility of our results.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34A09 | Implicit ordinary differential equations, differential-algebraic equations |
| 34G20 | Nonlinear differential equations in abstract spaces |
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
Keywords:
fixed point; implicit differential equations; existence; uniqueness; tempered fractional derivative; nonlocal conditionReferences:
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