Analysis of Hilfer fractional integro-differential equations with almost sectorial operators

In this work, we investigate a class of nonlocal integro-differential equations involving Hilfer fractional derivatives and almost sectorial operators. We prove our results by applying Schauder’s fixed point technique. Moreover, we show the fundamental properties of the representation of the solution by discussing two cases related to the associated semigroup. For that, we consider compactness and noncompactness properties, respectively. Furthermore, an example is given to illustrate the obtained theory.publishe

Generalized Mittag-Leffler stability of fractional impulsive differential system

This paper establishes sufficient conditions for Generalized Mittag-Leffler stability of a class of impulsive fractional differential system with Hilfer order. The analysis extends through both, instantaneous and non-instantaneous impulsive conditions. The theory utilizes continuous Lyapunov functions, to ascertain the stability conditions. An example is given discussing for various ranges

Nonlocal initial value problems for implicit differential equations with Hilfer–Hadamard fractional derivative

In this paper, the Schaefer's fixed-point theorem is used to investigate the existence of solutions to nonlocal initial value problems for implicit differential equations with Hilfer–Hadamard fractional derivative. Then the Ulam stability result is obtained by using Banach contraction principle. An example is given to illustrate the applications of the main result

Stability analysis of Hilfer fractional differential systems

In this paper, we present some remarks on the stability of fractional order systems with the Hilfer derivative. Using the Laplace transform, some sufficient conditions on the stability and asymptotic stability of autonomous and non-autonomous fractional differential systems are given. The results are obtained via the properties of Mittag-Leffler functions and the non-standard Gronwall inequality