In this paper, we investigate the exact and approximate controllability, finite time stability, β–Hyers–Ulam–Rassias stability of a fractional order neutral impulsive differential system. The controllability criteria is incorporated with help fixed point approach. famous generalized Grönwall inequality used to study stability. Finally, main results are verified an example.

Through literature retrieval and classification, it can be found that for the fractional delay impulse differential system, existence uniqueness of solution UHR stability system are rarely studied by using polynomial function matrix. In this paper, we firstly introduce a new concept impulsive delayed Mittag–Leffler type vector function, which helps us to construct representation an exact linear...

In this paper, we establish the existence and stability results for (?k,?k)-Hilfer fractional integro-differential equations under instantaneous impulse with non-local multi-point integral boundary conditions. We achieve formulation of solution to differential equation constant coefficients in term Mittag–Leffler kernel. The uniqueness result is proved by applying Banach’s fixed point theory pr...

In this paper, we prove the generalized Hyers-Ulam-Rassias stability of the generalized radical cubic functional equation[    fleft( sqrt[3]{ax^3 + by^3}right)=af(x) + bf(y),]    where $a,b in mathbb{R}_+$ are fixed positive real numbers, by using direct method in quasi-$beta$-Banach spaces. Moreover, we use subadditive functions to investigate stability of the generaliz...

moslehian  and mirmostafaee, investigated the fuzzystability problems for the cauchy additive functional equation, the jensen additivefunctional equation and the cubic functional equation in fuzzybanach spaces. in this paper, we investigate thegeneralized hyers–-ulam--rassias stability of the generalizedadditive functional equation with $n$--variables, in fuzzy banachspaces. also, we will show ...

We present a novel generalization of the Hyers–Ulam–Rassias stability definition to study generalized cubic set-valued mapping in normed spaces. In order achieve our goals, we have applied brand new fixed point alternative. Meanwhile, obtained practicable example demonstrating that is not defined as stable according previously methods and procedures.