Primene proširene Darboove teoreme o fiksnoj tački na frakcione diferencijalne jednačine sa konačnim kašnjenjem
Frakcione diferencijalne jednačine na neograničenim domenima
Sažetak
Uvod/cilj: Cilj rada je proučavanje postojanja blagih rešenja problema početne vrednosti Darbuovog problema za parcijalne hiperboličke frakcione diferencijalne jednačine pomoću Kaputovog izvoda sa konačnim kašnjenjem u Frešeovim prostorima.
Metode: U analizi se koriste Darboova teorema o fiksnoj tački i pojam mere nekompaktnosti kako bi se utvrdilo postojanje rešenja svođenjem istraživanja na dokazivanje postojanja i jedinstvenosti fiksnih tačaka odgovarajućih operatora.
Rezultati: Postojanje blagih rešenja posmatranih parcijalnih hiperboličkih frakcionih diferencijalnih jednačina je dokazano pod odgovarajućim uslovima. Primenljivost teorijskih rezultata je ilustrovana primerom.
Zaključak: U radu se razmatraju dovoljni uslovi za utvrđivanje postojanja i jedinstvenosti rešenja Darbuovog problema primenom Darboove teoreme o fiksnoj tački na neograničenom intervalu. Istraživanje pruža metodološki okvir za analizu sličnih problema i doprinosi širem razumevanju blagih rešenja u frakcionom računu i funkcionalnoj analizi. Dobijeni rezultati nude potencijalne primene za istraživače koji se bave frakcionim diferencijalnim jednačinama u beskonačno-dimenzionalnim prostorima.
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