Functional Equations with Causal Operators

Method of Nonsmooth Integral Guiding Functions in Periodic Solutions Problem for Inclusions with Causal Multioperators

“…[3]. Ðàçëè÷íûå çàäà÷è äëÿ ôóíêöèîíàëüíî-äèôôåðåíöèàëüíûõ óðàâíåíèé ñ êàóçàëüíûìè îïåðàòîðàìè áûëè ðàññìîòðåíû â ðàáîòàõ [410].…”

“…Ïðèíèìàÿ çà îñíîâó ñõåìó, ïðåäëîaeåííóþ â [3], ðàññìîòðèì ñëåäóþùóþ ìîäåëü óïðàâëÿåìîãî ÿäåðíîãî ðåàêòîðà. Áóäåì ñ÷èòàòü, ÷òî åãî äèíàìèêà îïèñûâàåòñÿ ñëå-äóþùåé ñèñòåìîé ôóíêöèîíàëüíî-îïåðàòîðíûõ óðàâíåíèé:…”

Terminal value problem for causal differential equations with a Caputofractional derivative

“…Recently, the study of differential equations [6] with causal operators [13] has rapidly developed and some results are assembled in [8,13,19,26]. The theory of causal operators is a powerful tool unifying the fractional order differential equations [4,16,25,27], ordinary differential equations [1,8,11,28], integro-differential equations [23], differential equations with finite or infinite delay, Volterra integral equations [23], and neutral functional equations [8,13,20].…”

Quasilinearization method for nonlinear differential equations with causal operators

“…All these equations are special cases of CDEs. The reader can consult [5,6] for a monograph on this subject with more details. After Corduneanu's work [6], a lot of research has been done on CDEs.…”

“…The reader can consult [5,6] for a monograph on this subject with more details. After Corduneanu's work [6], a lot of research has been done on CDEs. A systematic account of these developments and new extensions of CDEs in infinite dimensional spaces, fractional CDEs, set differential equations with causal operators and CDEs with retardation and anticipation, have been considered in detail by Lakshmikantham, founder of nonlinear federation, in [18].…”