Nonlocal problems for fractional integrodifferential equations via fractional operators and optimal controls

Fractional evolution equation nonlocal problems with noncompact semigroups

“…Since it is demonstrated that the nonlocal problems have are better in applications than the traditional Cauchy problems, differential equations with nonlocal conditions were studied by many authors and some basic results on nonlocal problems have been obtained, see [2,3,[6][7][8]10,13,17,21,22,29,31,32] and the references therein.…”

Existence of positive solutions for nonlocal boundary value problem of fractional differential equation

“…There are many papers dealing with the existence of solutions (for positive solutions) for boundary value problems of nonlinear fractional differential equations by the use of techniques of nonlinear analysis. Examples are, fixed point theorems, fixed point index theory, upper and lower solution method, etc, for the details, see [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. * E-mail: xipingliu@163.com…”

Existence results for boundary value problems of arbitrary order integrodifferential equations in Banach spaces

“…Examples and details concerning the development of the theory, methods and applications of fractional calculus can be found in the books [9], [11] and papers [1], [3], [4], [6], [7]. For some results on boundary value problems of fractional integrodifferential equations, we refer to the papers [2], [5], [12] and the references therein.…”