Method of semidiscretization in time to nonlinear retarded differential equations with nonlocal history conditions

Method of semidiscretization in time to nonlinear retarded differential equations with nonlocal history conditions

where 0< τ , T <∞, φ0 ∈ 0 := C([−τ,0];H), the nonlinear operator A is single valued andmaximalmonotone defined from the domainD(A)⊂H intoH, the nonlinearmap f is defined from [0,T ]×Hm+1 into H, the map h is defined from 0 into 0, and ψ[−τ,0] is the restriction of ψ ∈ T := C([−τ,T];H) on [−τ,0]. Here t := C([−τ,t];H) for t ∈ [0,T ] is the Banach space of all continuous functions from [−τ,t] int...

Applications of He’s Variational Principle method and the Kudryashov method to nonlinear time-fractional differential equations

  In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...

Solving nonlinear space-time fractional differential equations via ansatz method

In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...

Impulsive Functional-differential Equations with Nonlocal Conditions

On mild solutions to fractional differential equations with nonlocal conditions

We prove new existence results of mild solutions to fractional differential equations with nonlocal conditions in Banach spaces. The nonlocal item is only assumed to be continuous. This generalizes some recent results in this area.