This article deals with a class of nonlinear fractional differential equations, initial conditions, involving the Riemann–Liouville derivative order α∈(1,2). The main objectives are to obtain conditions for existence and uniqueness solutions (within appropriate spaces), analyze stabilities Ulam–Hyers Ulam–Hyers–Rassias types. In fact, different obtained based on analysis an associated integral ...

In this paper, we studied the Hyers–Ulam–Rassias stability of Hermite’s differential equation, using Pachpatte’s inequality. We compared our results with those obtained by Blaga et al. Our estimation for zx−yx, where z is an approximate solution and y exact was better than that authors previously mentioned, in some parts domain, especially a neighborhood origin.

Purpose This paper aims to study qualitative properties and approximate solutions of a thermostat dynamics system with three-point boundary value conditions involving nonsingular kernel operator which is called Atangana-Baleanu-Caputo (ABC) derivative for the first time. The results existence uniqueness solution such are investigated minimum hypotheses by employing Banach Schauder's fixed point...

‎In this paper‎, ‎using fixed point method‎, ‎we prove the generalized Hyers-Ulam stability of‎ ‎random homomorphisms in random $C^*$-algebras and random Lie $C^*$-algebras‎ ‎and of derivations on Non-Archimedean random C$^*$-algebras and Non-Archimedean random Lie C$^*$-algebras for‎ ‎the following $m$-variable additive functional equation:‎ ‎$$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...

A classical question in the theory of functional equations is “when is it true that a mapping, which approximately satisfies a functional equation, must be somehow close to an exact solution of the equation?” Such a problem, called a stability problem of the functional equation, was formulated by Ulam 1 in 1940. In the next year, Hyers 2 gave a partial solution of Ulam’s problem for the case of...

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...