Abstract The main aim of this paper is to investigate various types Ulam stability and Mittag-Leffler linear differential equations first order with constant coefficients using the Aboodh transform method. We also obtain Hyers–Ulam constants these some examples illustrate our results are given.

The aim of this paper is to consider the Hyers-Ulam stability of a class of parabolic equation { ∂u ∂t − a 2∆u+ b · ∇u+ cu = 0, (x, t) ∈ Rn × (0,+∞), u(x, 0) = φ(x), x ∈ Rn. We conclude that (i) it is Hyers-Ulam stable on any finite interval; (ii) if c 6= 0, it is Hyers-Ulam stable on the semi-infinite interval; (iii) if c = 0, it is not Hyers-Ulam stable on the semi-infinite interval by using ...

The Langevin system is an important mathematical model to describe Brownian motion. research shows that fractional differential equations have more advantages in viscoelasticity. exploration of dynamics novel and valuable. Compared with the Caputo or Riemann–Liouville (RL) derivatives, Mittag–Leffler (ML)-type derivatives can eliminate singularity such solution has better analytical properties....

This paper aims to study the existence and uniqueness of solution for nonlocal multiorder implicit differential equation involving Hilfer fractional derivative on unbounded domains a , ∞ ≥ 0 , in an applicable Banach...

In 1940 (and 1964) S. M. Ulam proposed the well-known Ulam stability problem. In 1941 D. H. Hyers solved the Hyers-Ulam problem for linear mappings. In 1992 and 2008, J. M. Rassias introduced the Euler-Lagrange quadratic mappings and the JMRassias “product-sum” stability, respectively. In this paper we introduce an Euler-Lagrange type quadratic functional equation and investigate the JMRassias ...

In this paper, we apply the well-known aggregation mappings on Mittag-Leffler-type functions to investigating new approximation error estimates of a W-Hilfer fractional differential equation, by different concept Ulam-type stability in both bounded and unbounded domains.

In this paper, we consider the newly defined partial (?,?)-fractional integral and derivative to study a new class of fractional differential equations with impulses. The existence Ulam-Hyers stability solutions for proposed equation are investigated via means measure noncompactness fixed point theorems. presented results quite general in their nature further complement existing ones.

This paper deals with the existence, uniqueness, and Ulam-stability outcomes for $\Xi$-Hilfer fractional fuzzy differential equations impulse. Further, by using techniques of nonlinear functional analysis, we study Ulam-Hyers-Rassias stability.

Abstract In the current manuscript, we combine q -fractional integral operator and derivative to investigate a coupled hybrid fractional -differential systems with sequential -derivatives. The existence uniqueness of solutions for proposed system are established by means Leray-Schauder’s alternative Banach contraction principle. Furthermore, Ulam-Hyers Ulam-Hyers-Rassias stability results discu...