Speaker: Rahma Yasmina Moulay Hachemi (University of Saida Dr. Moulay Tahar)
Title: The stochastic heat inclusion with fractional time derivative driven by time-space Brownian white noise
Abstract: We study a time-fractional stochastic heat inclusion driven by additive
time-space Brownian noise given by:
∂^α/∂t^α Y (t, x) ∈ λ∆Y (t, x) + G(t, x, Y (t, x)) + σW (t, x); (t, x) ∈ (0, ∞) × R^d.
Here d ∈ N = {1, 2, ...} is the space dimension, x ∈ R^d denotes a point in
space, t ≥ 0 denotes the time.
Here d ∈ N = {1, 2, ...} is the space dimension, x ∈ R^d denotes a point in
space, t ≥ 0 denotes the time. The fractional time derivative is interpreted as
the Caputo derivative of order α ∈ (0, 2). We show the following:
a) If a solution exists, then it is a fixed point of a specific set-valued map.
b) Conversely, any fixed point of this map is a solution of the heat inclusion.
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