Some New Existence Results and Stability Concepts for Fractional Partial Random Differential Equations

Abstract

In the present paper we provide some existence results and Ulam's type stability concepts for the Darboux problem of partial fractional random differential equations in Banach spaces, by applying the measure of noncompactness and a random fixed point theorem with stochastic domain.

On implicit fractional q‐difference equations: Analysis and stability

“…Random differential equations appear in many applications and have been studied by numerous mathematicians. For more information on this subject, we recommend the papers 32–37 …”

Solvability of Some Types for Multi-fractional Integro-Partial Differential Equation

“…The study of the existence of mild solution for an integro-differential equation description is as follows: Recently, the fractional order differential equation model is more interesting and more descriptive to be applied in various branches such as engineering and science. So, the abstract Cauchy problems with fractional order derivative simulated to some problems of the fractional differential equation have appeared in many articles for many applications in real life (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19). Consider the following fractional order integropartial differential equations: where 1 , 2 , > 0, ( , ) is denoted the deviation x at , 1 < ≤ 2, 1 < 1 + 2 ≤ 2 and 0 < 1 , 2 ≤ 1, ≥ 0, and is a Riemann-Liouville fractional derivative of order > 0, ∈ (X is a Banach space).…”