J. Vanterler da C. Sousa

Ulam–Hyers stability of a nonlinear fractional Volterra integro-differential equation

Using the

On the Ulam–Hyers–Rassias stability for nonlinear fractional differential equations using the \(\psi \)-Hilfer operator

\psi-

Two new fractional derivatives of variable order with non-singular kernel and fractional differential equation

Hilfer fractional derivative, we present a study of the Hyers-Ulam-Rassias stability and the Hyers-Ulam stability of the fractional Volterra integral-differential equation by means of fixed-point method.

Stability of ψ-Hilfer impulsive fractional differential equations

We study the existence and uniqueness of solution of a nonlinear Cauchy problem involving the

On the ψ-Hilfer fractional derivative

\psi

A New Truncated M-Fractional Derivative Type Unifying Some Fractional Derivative Types with Classical Properties

ψ-Hilfer fractional derivative. In addition, we discuss the Ulam–Hyers and Ulam–Hyers–Rassias stabilities of its solutions. A few examples are presented to illustrate the possible applications of our main results.

On two new operators in fractional calculus and application

In this paper, we introduce two new fractional derivatives with non-singular kernel and present a series of other fractional derivatives derived from the new formulations. We present some important results on uniformly convergent sequences of continuous functions with the help of the comparison principle and other results that allow the study of the limitation of the fractional nonlinear differential equation.

On a new operator in fractional calculus and applications.

Abstract In this paper, we investigate the sufficient conditions for existence and uniqueness of solutions and δ -Ulam–Hyers–Rassias stability of an impulsive fractional differential equation involving ψ -Hilfer fractional derivative. Fixed point approach is used to obtain our main results. Finally, we present examples to illustrate the results.