Existence and uniqueness of mild solutions to a semilinear integrodifferential equation of fractional order

Fractional finite time delay evolution systems and optimal controls in infinite-dimensional spaces

“…From Definition 3.1 we can find that mild definitions in [8,15,16,20,21] is inappropriate in that it is only a simple extension of the integer-order mild solutions.…”

Analysis of nonlinear Hadamard fractional differential equations via properties of Mittag–Leffler functions

“…The continuous time random walk theory is another example of arising of fractional derivatives in description of real physical systems (see [16]). There are several existence and stability results for all kinds of Caputo and Riemann-Liouville type nonlinear FDEs with constant coefficients (see [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]), and Hadamard type nonlinear FDEs without constant coefficient (see [1,Chapter 13] and [37][38][39][40][41][42][43]). However, the development of a related theory for Hadamard type nonlinear FDEs with constant coefficient is still in its infancy.…”

Existence of positive solutions for eigenvalue problem of nonlinear fractional differential equations

“…Recently, many results were obtained dealing with the existence and multiplicity of solutions of nonlinear fractional differential equations by the use of techniques of nonlinear analysis, see [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and the reference therein. Bai and Lu [7] studied the existence of positive solutions of nonlinear fractional differential equation …”