Nonlocal Cauchy problem for fractional evolution equations

Existence and controllability of fractional evolution equation with sectorial operator and impulse

“…Because nonlocal initial conditions generalize classical ones and play an important role in physics and engineering, more and more researchers pay attention to nonlocal Cauchy problems for different kinds of differential equations. For the fractional differential equations with nonlocal conditions, we refer to [18,23,42]. For the fractional differential equations with nonlocal conditions and impulsive effects, we refer to [13,14,21,37].…”

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.…”

Double image multi-encryption algorithm based on fractional chaotic time series

“…Fractional calculus, which dates back to the 17th century, has been applied to physics and engineering in recent decades [18,19]. A fractional-order system is characterized by a dynamical system described by fractional derivatives and integrals.…”