Existence of the mild solution for some fractional differential equations with nonlocal conditions

Existence of Asymptotically Almost Automorphic Mild Solutions of Semilinear Fractional Differential Equations

“…Many physical processes appear to exhibit fractional order behavior that may vary with time or space. In recent years, there has been a significant development in ordinary and partial differential equations involving fractional derivatives; we only enumerate here the monographs of Kilbas et al [26,27], Diethelm [28], Hilfer [29], Podlubny [30], Miller [31], and Zhou [32] and the papers of Agarwal et al [33,34], Benchohra et al [35,36], El-Borai [37], Lakshmikantham et al [38][39][40][41], Mophou et al [42][43][44][45], N'Guérékata [46], and Zhou et al [47][48][49][50] and the reference therein.…”

Mild Solutions to the Cauchy Problem for Some Fractional Differential Equations with Delay

“…It is well known (cf., e.g., [18]) that-A has a discrete spectrum with eigenvalues of the form n 2 , n ∈ N, and corresponding normalized eigenfunctions given by…”

“…As shown in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and the references therein, differential equations with delay or differential equations of fractional order have appeared in many branches of science and technology. They have received a lot of attention in all these years.…”

Nonlocal fractional functional differential equations with measure of noncompactness in Banach space

“…Indeed, the nonlocal initial condition xð0Þ ¼ / þ gðxÞ can be applied in physics with better effect than the classical initial condition xð0Þ ¼ /. For this reason, the problem (1.1) has gotten considerable attention in recent years, see [30][31][32] and the references therein. See also [33][34][35] and the references therein for recent generalizations of problem (1.1) to various kinds of differential equations.…”