Abstract Differential and Difference Equations

Abstract

This special issue of Advances in Difference Equations is devoted to highlight some recent developments in abstract differential equations, fractional differential equations, and difference equations and their applications to mathematical physics, engineering, and biology. It consists of 20 papers carefully selected through a rigorous peer review. The first category of papers deals with the asymptotic and oscillatory behavior of solutions to various abstract differential equations and fractional differential equations. Periodic problems involving the scalar p-Laplacian equation on time scales, or n-species nonautonomous food chains with harvesting terms are studied using the Mawhin’s continuation theorem. Some new oscillation criteria for the second-order quasilinear neutral delay dynamic equations and nonlinear delay dynamic equations on a time scale T, are established, improving some known results for oscillation of second-order nonlinear delay dynamic equations on time scales. The study of almost automorphic functions in Bochner’s sense have attracted several mathematicians since the publication of N’Guerekata’s book in 2001. Recently, their applications to fractional differential equations have become an emerging field. A new and general existence and uniqueness theorem of almost automorphic solutions for the semilinear fractional differential equation