Existence of mild solutions for multi-term time fractional measure differential equations. (English) Zbl 1497.34089
Summary: This paper focuses on a class of multi-term time-fractional measure differential equations involving nonlocal conditions. A set of sufficient conditions for the existence of mild solutions is provided. Utilizing \((\beta,\gamma_k)\)-resolvent family in the sense of Pardo and Lizama, measure functional (Henstock-Lebesgue-Stieltjes integral) and Schauder’s fixed point theorem, we prove the existence of mild solutions. Finally, an illustrated example is presented.
MSC:
| 34G20 | Nonlinear differential equations in abstract spaces |
| 34K37 | Functional-differential equations with fractional derivatives |
| 39A99 | Difference equations |
| 46G99 | Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) |
Keywords:
regulated functions; Henstock-Lebesgue-Stieltjes integral; fractional calculus; generalized semigroup theory; multi-term time-fractional; fixed point theoryReferences:
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