Fractional partial random differential equations with infinite delay

On Nonlinear Periodic Problems with Caputo's Exponential Fractional Derivative

“…Fractional calculus is a generalization of ordinary dierentiation and integration to arbitrary order. For additional information check, for example, the books ( [1,2,8,9,33]), the papers [12,15,17,22,25,26,38,37,36,35,3,4,5,6,7] and the references therein.…”

Functional k-Generalized Ψ-Hilfer Fractional Differential Equations in b-Metric Spaces

“…Fractional differential equations have recently been applied in various areas of engineering, mathematics, physics, and other applied sciences. Considerable attention has been given to the existence of solutions of initial and boundary value problems for fractional differential and integral equations; see the publications [1,3,4,15,18,21,22,[25][26][27][28][29][30][31].…”

On a class of nonlinear time‐fractional pseudo‐parabolic equations with bounded delay

“…For more meaningful works about the delay, one may refer to the recent papers. [31][32][33][34] Very recently, Xu et al 35 have addressed the following nonautonomous nonlocal parabolic equation when the external force term contains hereditary characteristics involving bounded or infinite delays…”

“…The time‐lag effect is ubiquitous in real life because any process consumes time, no matter how long or short the process is. For more meaningful works about the delay, one may refer to the recent papers 31–34 . Very recently, Xu et al 35 have addressed the following nonautonomous nonlocal parabolic equation when the external force term contains hereditary characteristics involving bounded or infinite delays $$$$ \left\{\begin{array}{ll}\frac{\partial u}{\partial t}-a\left(l(u)\right)\Delta u=f(u)+h\left(t,{u}_t\right),& x\in \Omega, t\in \left[{t}_0,\infty \right),\\ {}u\left(x,t\right)=0,& x\in \mathrm{\partial \Omega },t\in \left[{t}_0,\infty \right),\\ {}u\left(x,{t}_0+\theta \right)=\varphi \left(x,\theta \right),& x\in \Omega, \theta \in \left(-\tau, 0\right],\end{array}\right.$$…”