A Borsuk–Ulam type argument is used in order to prove existence of nontrivial bounded solutions to some nonautonomous linear differential equations.

In this paper, we prove the generalized Hyers–Ulam stability of a quadratic and quartic functional equation in intuitionistic fuzzy Banach spaces.

The aim of this article is to proved a Mazur-Ulam type theorem in the strictly convex fuzzy anti-normed spaces.

S. M. Ulam’s contributions to biology are surveyed. The survey covers cellular automata theory, population biology, Fermi-Pasta-Ulam results, pattern recognition, and sequence similarity.

We prove the generalized Hyers-Ulam stability of the one-dimensional wave equation, u(tt) = c(2)u(xx), in a class of twice continuously differentiable functions.

We solve the inhomogeneous Chebyshev’s differential equation and apply this result to obtain a partial solution to the Hyers-Ulam stability problem for the Chebyshev’s differential equation.

In this paper, we prove the generalized Hyers–Ulam stability of homomorphisms and (θ, φ)-derivations on a ring R into a Banach R-bimodule M.

In this current paper, using q-fractional calculus, we study the Duffing–Rayleigh type problem with sequential fractional q-derivative of Caputo type. We investigate existence and uniqueness solutions by applying some classical fixed point theorems. Also define Ulam–Hyers Ulam–Hyers–Rassias stabilities for our problem. An example is presented to illustrate main results.

Abstract This article discusses the stability results for solution of a fractional q -integro-differential problem via integral conditions. Utilizing Krasnoselskii’s, Banach fixed point theorems, we demonstrate existence and uniqueness results. Based on obtained, conditions are provided to ensure generalized Ulam Ulam–Hyers–Rassias stabilities original system. The illustrated by two examples.