Three-Point Boundary Value Problems of Coupled Nonlocal Laplacian Equations

This paper discusses a kind of coupled nonlocal Laplacian evolution equation with Caputo time-fractional derivatives and proportional delays. Green function mild solution are firstly established by employing the approach eigenvalues’ expansions Fourier analysis technique. By properties eigenvalues Mittag–Leffler functions, several vital estimations functions presented. In view these some appropriate assumptions, existence uniqueness studied utilizing Leray–Schauder fixed-point theorem Banach theorem. Finally, an example is provided to illustrate effectiveness our main results.