We study the approximate solution of special type \(n^{th}\) order linear differential equation by applying initial and boundary conditions using Taylor's series formula. That is, we prove sufficient condition for Mittag-Leffler-Hyers-Ulam stability Mittag-Leffler-Hyers-Ulam-Rassias higher with

Abstract In this paper, we investigate the existence and uniqueness of a solution for class ψ -Hilfer implicit fractional integro-differential equations with mixed nonlocal conditions. The arguments are based on Banach’s, Schaefer’s, Krasnosellskii’s fixed point theorems. Further, applying techniques nonlinear functional analysis, establish various kinds Ulam stability results analyzed problem,...

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 ...

In the current manuscript, we study uniqueness and Ulam-stability of solutions for sequential fractionalpantograph differential equations with nonlocal boundary conditions. The is es-tablished by Banach's fixed point theorem. We also define Ulam-Hyers stability theUlam-Hyers-Rassias mentioned problem. An example presented to illustrate main results.

Abstract A thermostat model described by a second-order fractional difference equation is proposed in this paper with one sensor and two sensors boundary conditions depending on positive parameters using the Lipschitz-type inequality. By means of well-known contraction mapping Brouwer fixed-point theorem, we provide new results existence uniqueness solutions. In work use Caputo operator Hyer–Ul...

In 1940 and 1964, Ulam proposed the general problem: “When is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true?”. In 1941, Hyers solved this stability problem for linear mappings. According to Gruber 1978 this kind of stability problems are of the particular interest in probability theory and in ...

The Laplace transform method is applied to study the semi-Hyers–Ulam–Rassias stability of a Volterra integro-differential equation second order. A general formulated first; then, some particular cases for function from kernel are considered.

In this paper, the existence of solution and its stability to fractional boundary value problem (FBVP) were investigated for an implicit nonlinear differential equation (VOFDE) variable order. All criteria solutions in our establishments derived via Krasnoselskii’s fixed point theorem sequel, Ulam–Hyers–Rassias (U-H-R) is checked. An illustrative example presented at end paper validate findings.

In 1940, Ulam [9] gave a wide ranging talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of important unsolved problems. Among those was the following question concerning the stability of homomorphisms. Let G1 be a group and let G2 be a metric group with a metric d(·,·). Given ε > 0, does there exist a δ > 0 such that if a function h : G1 → G2 satisfi...