The second-order nonlinear oscillators have rich dynamics. We proposed a novel analytical method based on both variational iteration method and Adomian method. The variational iteration method is used to establish an equivalent integral system. So then Adomian polynomials are adopted to linearize the strong nonlinear terms in nonlinear oscillators and analytical solutions are obtained successively.
Maximum and minimum principles for time-fractional Caputo-Katugampola diffusion operators are proposed in this paper. Several inequalities are proved at extreme points. Uniqueness and continuous dependence of solutions for fractional diffusion equations of initial-boundary value problems are considered.
The purpose of this paper is devoted to consider the existence of solutions for a class of nonlinear Caputo-Hadamard fractional differential equations with integral terms ((CHFDE), for short). Firstly, by applying the semi-group property of Hadamard fractional integral operator, a necessary condition of solvability for (CHFDE) is established. Then, under the suitable conditions, we prove the solution set of (CHFDE) is nonempty by using the method of upper and lower solutions, and Arzelà-Ascoli theorem. Finally, we present several numerical examples to explicate the main results.
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