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This paper deals with the existence of solution for an impulsive Riemann–Liouville fractional neutral functional stochastic differential equation with infinite delay of order 1<β<2 and its Hyers–Ulam stability. We prove the mild solutions for the equation using basic theorems of fractional differential equation. The existence result of the equation is obtained by Mönch’s fixed...
In this paper, we study the existence and uniqueness of solution (EUS) as well as Hyers-Ulam stability for a coupled system of FDEs in Caputo’s sense with nonlinear p-Laplacian operator. For this purpose, the suggested coupled system is transferred to an integral system with the help of four Green functions G α 1 ( t , s ) $\mathcal{G}^{\alpha_{1}}(t,s)$ , G β 1 ( t , s ) $\mathcal{G}^{\beta_{1}}(t,s)$...
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