id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-856	Agarwal, Ravi ; Baltaeva, Umida; Hubert, Florence; Khasanov, Boburjon 	Existence and uniqueness of  the solution to initial and inverse problems for integro-differential heat equations with fractional load	2024	19	.pdf	application/pdf	7840	426	75	Fractional diffusion equations are extensions of the basic equations of mathe- matical physics Find a solution u(x, t) in the domain (x, t) ∈ Rn T of the loaded heat equation ut − a(t)∆u = λD−α 0t u(x ′, t) + ∫ t 0 k(x′, τ)u(x, t− τ)dτ, (x, t) ∈ Rn T , (2.1) that satisfies the condition u(x, t) ∣∣ t=0 = φ(x), x ∈ Rn, (2.2) where D−α 0t is the Riemann-Liouville fractional integral operator of order α defined by D−α 0t u(x ′, t)	cache/ejde-856.pdf	txt/ejde-856.txt