Existence and uniqueness of mild solution of time-fractional semilinear differential equations with a nonlocal final condition

Existence and uniqueness of mild solution of time-fractional semilinear differential equations with a nonlocal final condition

In this paper, we investigate a time-fractional semilinear differential equation with final nonlocal condition u(x,T)−(Gu)(x)=∑j=1mϑju(x,tj). Under some assumptions, we establish the existence and uniqueness of a mild solution in some suitable spaces of continuous functions. The results are based on...

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Veröffentlicht in:Computers & mathematics with applications (1987) 2019-09, Vol.78 (5), p.1651-1668
Hauptverfasser: Tuan, Nguyen Huy, Ngoc, Tran Bao, Huynh, Le Nhat, Kirane, Mokhtar
Format: Artikel
Sprache:eng
Schlagworte:
Continuity (mathematics)
Differential equations
Fixed point theory
Fixed points (mathematics)
Fractional diffusion equation
Nonlocal problem
Uniqueness
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Beschreibung
Zusammenfassung:In this paper, we investigate a time-fractional semilinear differential equation with final nonlocal condition u(x,T)−(Gu)(x)=∑j=1mϑju(x,tj). Under some assumptions, we establish the existence and uniqueness of a mild solution in some suitable spaces of continuous functions. The results are based on some fixed point theorems. Two examples are presented to illustrate our results.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2018.11.007