On the approximate controllability of neutral integro-differential inclusions of Sobolev-type with infinite delay

Abstract

In our manuscript, we organize a group of sufficient conditions of neutral integro-differential inclusions of Sobolev-type with infinite delay via resolvent operators. By applying Bohnenblust-Karlin's fixed point theorem for multivalued maps, we proved our results. Lastly, we present an application to support the validity of the study.

Results on approximate controllability results for second‐order Sobolev‐type impulsive neutral differential evolution inclusions with infinite delay

“…Byszewski [53, 54] introduced the concept of nonlocal conditions to study the existence of mild solutions for differential systems. Several researchers done enormous works inspired by these articles; one can refer to [5, 9, 10, 27, 41, 53, 54]. Consider the second‐order Sobolev‐type impulsive differential inclusions along with nonlocal conditions has the form …”

“…The controllability problem is finding an appropriate control function to such a degree that one can steer the considered dynamical system to a final state. Accordingly, over recent years, the discussion about the controllability of numerous nonlinear frameworks has been comprehensively investigated by many researchers and one can view the articles, for instance, [4,[11][12][13][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”

A new exploration on existence of Sobolev‐type Hilfer fractional neutral integro‐differential equations with infinite delay

“…Sobolev-type differential systems commonly manifest in the mathematical form of numerous physical phenomena similar to fluid flow over fissured rocks, thermodynamics. So on, we can refer to [19,[32][33][34][35][36][37][38][39][40]. To the best of our knowledge, the existence of mild solutions for Sobolev-type Hilfer fractional neutral integro-differential equations with infinite delay has not been studied in this connection.…”

A new study on existence and uniqueness of nonlocal fractional delay differential systems of order 1 < r < 2 in Banach spaces

“…Many excellent monographs give the essential conceptual instruments to the subjective assessment of this investigation area. On the other hand, showing the interlinking similarly as the separation among classical and fractional differential representations, the readers can refer the monographs [1–5] and the research articles [6–22,37].…”

“…When comparing nonlocal initial condition with the classical initial condition, which is more accurate to depict the nature marvels, since more information is considered, with these lines lessening the negative impacts initiated by a potential incorrect single estimation taken toward the beginning time. Very useful discussion about differential systems including nonlocal conditions, one can refer [7,8,11,12,15,22,[25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”