Pseudo S-asymptotically Bloch type periodic solutions to fractional integro-differential equations with Stepanov-like force terms

Weighted pseudo S-asymptotically Bloch type periodic solutions for a class of mean field stochastic fractional evolution equations

“…Finally, we relax the Lipschitz condition of g to some sublinear growth conditions (see Theorem 3.14). Consequently, our research study can be viewed as an extension and continuation of investigation in [5,6,8,9,24,35,36,38]. Additionally, this work generalize various papers on S-asymptotically ω-antiperiodic (or ω-periodic) mild solutions of to square-mean weighted pseudo S-asymptotically (ω, k)-periodic mild solutions for some stochastic fractional evolution equations.…”

“…Moreover, if f ≡ 0 and g(t, v(t), P v(t) ) ≡ g(t, v(t)), the existence and uniqueness of almost automorphic, asymptotically periodic, almost periodic, asymptotically ω-periodic solutions, S-asymptotically ω-periodic solutions, asymptotically almost periodic and asymptotically almost automorphic, (ω, c)-periodic and pseudo S-asymptotically (ω, k)-Bloch periodic mild solutions of problem (1.1) have been investigated in deterministic cases by various authors [6,8,9,24,35,36,38]. In this work, the problem (1.1) captures fading memory behaviors, and randomness of the dynamical processes.…”

$$(\omega ,Q)$$-periodic mild solutions for a class of semilinear abstract differential equations and applications to Hopfield-type neural network model

“…On the other hand, various authors have published works related with different variants and generalizations of periodic functions, namely, (ω, c)-pseudo periodic functions, (ω, c)-asymptotically periodic functions, c-semiperiodic and c-almost periodic functions, pseudo S-asymptotically Bloch type periodic functions, among others (see [1][2][3][4][5]8,[18][19][20][21][22]).…”