Abd Elhakim Lamairia, "Nonexistence Results of Global Solutions for Fractional Order Integral Equations on the Heisenberg Group," WSEAS Transactions on Systems, vol. 21, pp. 382-386, 2022, DOI:10.37394/23202.2022.21.42
Abd Elhakim Lamairia. Nonexistence Results of Global Solutions for Fractional Order Integral Equations on the Heisenberg Group.
WSEAS Transactions on Systems. 2022;21:382-386. 10.37394/23202.2022.21.42
WSEAS Transactions on Systems
Print ISSN: 1109-2777, E-ISSN: 2224-2678
Volume 21, 2022
Nonexistence Results of Global Solutions for Fractional Order Integral Equations on the Heisenberg Group
Author:
Abstract: We consider the fractional order integral equation with a time nonlocal nonlinearity $${^c} \textbf {D}{^β_{0|t}}(u)+(-Δ_{\mathbb{H}})^{m}(u)=\frac{1}{Γ(α)}\int_{0}^{t}(t-w)^{α-1}|u(w)|^{p}dw$$, posed in $$(.,t)\in\mathbb{H}$$x$$(0,\infty)$$, supplemented with an initial data $$u(.,0)=u_{0}(.)$$, where $$m>1, p>1, 0<β<1,0<α<1$$, and $${^c} \textbf {D}{^β_{0|t}}$$ denotes the caputo fractional
derivative of order $$β,$$ and $$Δ_{\mathbb{H}}$$ is the Laplacian operator on the $$(2N+1)$$-dimensional. Heisenberg group $$\mathbb{H}$$. Then, we prove a blow up result for its solutions.
Pages: 382-386 WSEAS Transactions on Systems, ISSN / E-ISSN: 1109-2777 / 2224-2678, Volume 21, 2022, Art. #42 DOI: 10.37394/23202.2022.21.42
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