An alternative method for the study of impulsive differential equations of fractional orders in a Banach space. (English) Zbl 1295.34009
Summary: This paper is concerned with the existence, uniqueness, and stability of the solution of some impulsive fractional problem in a Banach space subjected to a nonlocal condition. Meanwhile, we give a new concept of a solution to impulsive fractional equations of multiorders. The derived results are based on Banach’s contraction theorem as well as Schaefer’s fixed point theorem.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34G20 | Nonlinear differential equations in abstract spaces |
| 34B37 | Boundary value problems with impulses for ordinary differential equations |
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
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