Unique Solution for Multi-point Fractional Integro-Differential Equations
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DOI: 10.1515/ijnsns-2019-0042
Abstract: Abstract We study a fractional integro-differential equation subject to multi-point boundary conditions: D0+αu(t)+f(t,u(t),Tu(t),Su(t))=b, t∈(0,1),u(0)=u′(0)=⋯=u(n−2)(0)=0,D0+pu(t)|t=1=∑i=1maiD0+qu(t)|t=ξi, $$\left\{\begin{array}{l} D^\alpha_{0^+} u(t)+f(t,u(t),Tu(t),Su(t))=b,\ t\in(0,1),\\u(0)=u^\prime(0)=\cdots=u^{(n-2)}(0)=0,\\ D^p_{0^+}u(t)|_{t=1}=\sum\limits_{i=1}^m a_iD^q_{0^+}u(t)|_{t=\xi_i},\end{array}\right.$$ where α∈(n−1,n], n∈N, n≥3, ai≥0, 00 $\alpha\in (n-1,n],\ n\in \textbf{N},\ n\geq 3,\ a_i\geq 0,\ 0 read more here.
Keywords: integro differential; multi point; unique solution; fractional integro ... See more keywords