Existence and uniqueness of solutions for fractional nonlinear hybrid impulsive system. (English) Zbl 1536.34006
Summary: The investigation of existence and uniqueness of impulsive dynamical fractional systems with quadratic perturbation of second type subject to nonlocal boundary conditions is presented and proved. By employing the fractional theory, Banach contraction technique, and Krasnoselskii’s fixed point theorem, we derived some sufficient conditions to ensure the existence of our system. An example is offered to enhance the applicability of the results obtained.
{© 2020 Wiley Periodicals LLC}
{© 2020 Wiley Periodicals LLC}
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34A37 | Ordinary differential equations with impulses |
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 34B37 | Boundary value problems with impulses for ordinary differential equations |
| 47H10 | Fixed-point theorems |
| 34A38 | Hybrid systems of ordinary differential equations |
| 34D10 | Perturbations of ordinary differential equations |
Keywords:
fixed point theorems; fractional derivatives and integrals; hybrid differential equations; impulsive conditions; nonlocal boundary conditionsReferences:
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