New Study of the Existence and Dimension of the Set of Solutions for Nonlocal Impulsive Differential Inclusions with a Sectorial Operator

Abstract

In this article, we are interested in a new generic class of nonlocal fractional impulsive differential inclusions with linear sectorial operator and Lipschitz multivalued function in the setting of finite dimensional Banach spaces. By modifying the definition of PC-mild solutions initiated by Shu, we succeeded to determine new conditions that sufficiently guarantee the existence of the solutions. The results are obtained by combining techniques of fractional calculus and the fixed point theorem for contraction maps. We also characterize the topological structure of the set of solutions. Finally, we provide a demonstration to address the applicability of our theoretical results.

Existence and controllability of fractional evolution inclusions with impulse and sectorial operator

“…Many researchers are concerned with non-local Cauchy problems for dierent types of dierential equations and inclusions because the nonlocal initial conditions generalize classical terms and play an important role in engineering and physics. For nonlocal fractional dierential equations and inclusions see [5,6,7,13,15,26,25].…”

“…Recently,the topic of inclusions of evolution and equations involving sectorial or almost sectorial terms has been extensively studied ( see [2,7,30,31,32,34,35,37]). For instance, Shu et al [31] introduced a dierent concept of mild solutions for (1) when F is a completely continuous single-valued function and A is a sectorial operator with {S α (t) : t ≥ 0} and {T α : t ≥ 0} are compact.…”

A note on the existence of Hilfer fractional differential inclusions with almost sectorial operators

“…Alsarori et al 34 interested in a new generic class of nonlocal fractional impulsive differential inclusions with linear sectorial operator and Lipschitz multivalued function in the setting of finite dimensional Banach spaces. Researchers have done enormous achievements related to sectorial operators in previous studies.…”

Editorial Conclusion for the Special Issue “Fixed Point Theory and Computational Analysis with Applications”

“…Fixed point theory and applications (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]); • Computational analysis and applications (see [1,2,7,9,12,[15][16][17][18][19][20][21][22][23][24][25]).…”