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Maximal ℓ p ‐regularity of multiterm fractional equations with delay
Author(s) -
Girona Ivan,
MurilloArcila Marina
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6792
Subject(s) - mathematics , uniqueness , banach space , nonlinear system , fractional calculus , mathematical analysis , space (punctuation) , order (exchange) , domain (mathematical analysis) , derivative (finance) , characterization (materials science) , operator (biology) , fréchet derivative , pure mathematics , physics , chemistry , linguistics , philosophy , biochemistry , finance , repressor , quantum mechanics , transcription factor , financial economics , optics , economics , gene
We provide a characterization for the existence and uniqueness of solutions in the space of vector‐valued sequencesℓ p ( ℤ , X ) for the multiterm fractional delayed model in the formΔ α u ( n ) + λ Δ β u ( n ) = A u ( n ) + u ( n − τ ) + f ( n ) , n ∈ ℤ , α , β ∈ ℝ + , τ ∈ ℤ , λ ∈ ℝ , where X is a Banach space, A is a closed linear operator with domain D ( A ) defined on X , f ∈ ℓ p ( ℤ , X ) and Δ Γ denotes the Grünwald–Letkinov fractional derivative of order Γ > 0. We also give some conditions to ensure the existence of solutions when adding nonlinearities. Finally, we illustrate our results with an example given by a general abstract nonlinear model that includes the fractional Fisher equation with delay.