Semigroups and some nonlinear fractional differential equations

Existence and uniqueness of mild solutions to initial value problems for fractional evolution equations

“…El-Borai [5][6][7] used a probability density function to obtain the solutions to Cauchy problems for different fractional evolution equations. In 2010, Hernandez et al [8] proved that the concepts of mild solutions of fractional evolution equations considered in some previous papers were not appropriate.…”

Hölder Regularity for Abstract Fractional Cauchy Problems with Order in (0,1)

“…details we refer to [7] [8] [9]. The vector-valued Laplace transform developed in [3] is an important tool in the theory of fractional differential equations.…”

Fractional Evolution Integrodifferential Systems with Nonlocal Conditions in Banach Spaces

“…The Fractional differential equations have been studied with more interest by many authors [8,12,14,15,16,17,18,20,22,25] in the recent times as they effectively describe many phenomena arising in engineering, physics, economy and science including several applications in the fields of viscoelasticity, electrochemistry, electro-magnetic, and so on. The existence of solutions to evolution equations with nonlocal conditions in Banach space was established first by Byszewski [9].…”