Semilinear fractional differential equations with infinite delay and non-instantaneous impulses

Existence of solutions of non-autonomous fractional differential equations with integral impulse condition

“…3 Post Graduate and Research Department of Mathematics, Kongunadu Arts and Science College (Autonomous), Coimbatore 641 029, Tamil Nadu, India. 4 Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawasir 11991, Saudi Arabia. 5 Department of Mathematics, Cankaya University, Ankara, Turkey.…”

“…From the past two decades, fractional calculus has attracted research attention towards itself due to its importance in several parts of science, like physics, fluid mechanics, heat conduction [1,19,21,24,26,27,32,33,[37][38][39][40][41][42]. We can relate to the monographs [2,22,30,36] for the fundamentals and to [4,44,45] for the current developments in the field of fractional calculus.…”

Boundedness, periodicity, and conditional stability of noninstantaneous impulsive evolution equations

“…1 Existence and stability results for this new type of impulsive equations have been reported in previous works. [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] Periodic solutions of noninstantaneous impulsive equations were studied in previous literature, [22][23][24] and existence results were established by constructing a suitable composite Poincaré operator through some compact embeddings. [25][26][27] A strong contraction condition appeared in the main theorems; see Fečkan et al, 22, Theorem 2.5, Wang et al, 23, Theorem 4 and Muslim et al 24, Theorem 3.7.…”

A remark on ψ–Hilfer fractional differential equations with non‐instantaneous impulses

“…12 Up to now, extensive works have been presented in the area of non-instantaneous impulses, and there has been a significant development in the qualitative theory of the Cauchy problems of differential equations with the concepts of integer-order derivative and fractional-order derivative. For more recent development on this topic, one can see the papers of Bai and Nieto, 13 Benchohra el al, 14 Chen et al, 15 Sousa et al, 9 Wang et al, 16 Liu et al, 17 and the references cited therein.…”