Existence of solution for Volterra–Fredholm type stochastic fractional integro‐differential system of order μ ∈ (1, 2) with sectorial operators

• Published in: Mathematical methods in the applied sciences Vol. 46; no. 12; pp. 13142 - 13154
• Main Authors: Kaliraj, K., Muthuvel, K.
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 01.08.2023
• Subjects: fixed‐point techniques; mild solutions; sectorial operators; stochastic differential systems
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.9240

The mainspring of the study is to investigate the out‐turn of stochastic Volterra–Fredholm integro‐differential inclusion of order μ∈(1,2)$$ \mu \in \left(1,2\right) $$ with sectorial operator of the type (P,η,ϱ,γ)$$ \left(P,\eta, \varrho, \gamma \right) $$. The existence results of our proposed problem is derived by employing Martelli's fixed point approach. We do not limit the theoretical results of fractional stochastic equation to local condition but extend to nonlocal condition, and physical interpretation of our obtained results is proved with an appropriate illustration.