Theory and Modern Applications
α,β | Corresponding reduced BVPs |
---|---|
β: = 1 | \((\mathcal{D}_{a^{+}}^{\alpha,\beta }u )(t)=-h(t), u(a)=u(b)=0\longrightarrow ^{c}\mathcal{D}_{a^{+}}^{\alpha }u(t)=-h(t), u(a)=u(b)=0\) |
β: = 0 | \((\mathcal{D}_{a^{+}}^{\alpha,\beta }u )(t)=-h(t), u(a)=u(b)=0\longrightarrow \mathcal{D}_{a^{+}}^{\alpha }u(t)=-h(t), u(a)=u(b)=0\) |
α: = 2 | \((\mathcal{D}_{a^{+}}^{\alpha,\beta }u )(t)=-h(t), u(a)=u(b)=0\longrightarrow u^{\prime \prime }(t)=-h(t), u(a)=u(b)=0\) |