Well-posedness of nonlinear fractional quadratic iterative differential equations. (English) Zbl 1510.34029
Summary: In this paper, we discuss the existence and uniqueness of solutions for a class of nonlinear fractional quadratic iterative differential equations in Banach space \(C([0, T], [0, T])\), \(C_{L_T}([0,T],[0,T])\), and \(C_{L_A}([0,T],[0,T])\), respectively. Our analysis is based on Schauder’s fixed point theorem, fractional Gronwall inequalities and Picard operator theory. Furthermore, our results can be extend to extra complex nonlinear terms. Finally, some examples are given to illustrate our results.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 47H10 | Fixed-point theorems |
Keywords:
iterative fractional differential equations; fractional Gronwall inequalities; fixed point theorem; existenceReferences:
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