Existence of anti-periodic mild solutions for a class of semilinear fractional differential equations

Study of implicit type coupled system of non‐integer order differential equations with antiperiodic boundary conditions

“…On the other hand, theory/concept of antiperiodic BCs have been quite significant in the recent years, more specifically in the mathematical modeling of certain phenomena and physical processes like wavelets, physics, and in dealing with interpolation problems with trigonometric polynomials . A significant work has been done on antiperiodic BVPs with fractional orders as cited in the previous studies …”

“…This concept can be employed in linear and nonlinear problems arising in differential and integral equations both, see other studies . For the first time in 1997, Obloza introduced the UHS for linear differential equations, see other studies . After that, lot of work has been carried out on it.…”

Existence of Asymptotically Almost Automorphic Mild Solutions of Semilinear Fractional Differential Equations

“…He et al [58] studied also the existence and uniqueness of weighted Stepanov-like pseudo almost automorphic mild solution to (2). Cao et al [59] studied the existence and uniqueness of antiperiodic mild solution to (2). In [60], Cuevas et al showed sufficient conditions to ensure the existence and uniqueness of mild solution for (2) in the following classes of vector-valued function spaces: periodic functions, asymptotically periodic functions, pseudo periodic functions, almost periodic functions, asymptotically almost periodic functions, pseudo almost periodic functions, almost automorphic functions, asymptotically almost automorphic functions, pseudo almost automorphic functions, compact almost automorphic functions, asymptotically compact almost automorphic functions, pseudo compact almost automorphic functions, -asymptotically -periodic functions, decay functions, and mean decay functions.…”

“…However, in many papers (for instance, [11,[51][52][53][54][55][56][57][58][59][60][61][62][63][64]) on almost periodic type and almost automorphic type solutions to fractional differential equations, to be able to apply the well-known Banach contraction principle, a (locally) Lipschitz condition for the nonlinearity of corresponding fractional differential equations is needed. As can be seen, our results generalize those as well as related research and have more broad applications.…”

“…For this reason, (6) has gotten a considerable attention in recent years (cf. [51][52][53][54][55][56][57][58][59][60][61][62][63][64][68][69][70][71] and the references therein).…”