Existence and stability of solution for a nonlinear fractional differential equation

Existence and stability results for nonlinear fractional integro-differential coupled system

“…To prove the general existence and stability results, we impose special growth conditions on function f and K extend the works given by [34,35].…”

Novel Results on Finite‐Time Stability of Solutions for Stochastic Ψ‐Hilfer Fractional System

“…With the aid of Grönwall approach, Luo and Luo [41] researched the fnite-time stability of Ψ-Hilfer fractional impulsive delay system. In addition, Zhou et al [42] and Luo et al [43] established the existence of solutions and stability results for Ψ-Hilfer fractional system. Under the non-Lipschitz assumption, using the Laplace transform and its inverse, Luo et al [44] considered a kind of stochastic Hilfer-type fractional system.…”

“…For more knowledge about Hilfer fractional calculus, one can refer to [1,45]. Compared with the references [41][42][43][44], in this article, we will investigate the stochastic Ψ-Hilfer fractional system. According to all the studies we known, there are few results on Ψ-Hilfer fractional system driven by random process.…”

“…(1) Compared with [42], the proposed model in present manuscript is more generalized, in which the random term is considered in Ψ-Hilfer fractional system. Tere are few literatures available for solving this type of considered system.…”

Studying the Stability of the ψ‐Hilfer Fractional Differential System

“…In the last five decades, fractional differential equations (FDEs) have attracted great attention from researchers since FDEs may acquire more accurate results than the integerorder differential equations, especially for the description of materials and processes charactering memorial and hereditary properties [1][2][3][4]. Some authors studied works on existence, uniqueness, and data dependence of solution to FDEs [5][6][7][8][9][10][11], while another scholars focused on stability results of FDEs (including linear and nonlinear cases) with different types of fractional derivatives [12][13][14][15][16][17][18].…”