Existence of the mild solution for some fractional differential equations with nonlocal conditions

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New discussion on approximate controllability results for fractional Sobolev type Volterra‐Fredholm integro‐differential systems of order 1 < r < 2 (2021, background): “A broad list of these distributions can be discovered in [6, 9, 11–16, 18–24, 43, 44–50].”
Existence Results for Fractional Order Semilinear Integro-Differential Evolution Equations with Infinite Delay (2010, background): “The theory of fractional order differential equations has become an active area of investigation due to their applications in the fields such as physics, technical sciences and so on. One can see Anguraj [1], Lakshmikantham and his co-authors [14,15], Hu et al. [10], Mophou and N’Gu´ er´ ekata [18, ”