In this paper, the authors have proposed the qualitative properties for the solution of the
Hilfer implicit fractional differential equations (HIFDE) of order 1< ϱ≤ 2 involving nonlocal …

Fractional calculus with respect to function $\psi $, also named as $\psi $-fractional calculus,
generalizes the Hadamard and the Riemann-Liouville fractional calculi, which causes …

Although many applications of fractional calculus have been reported in literature, modeling
the physical world using this technique is still a challenge. One of the main difficulties in …

In this paper, the nonlinear version of the Henry–Gronwall integral inequality with the
tempered Ψ-Hilfer fractional integral is proved. The particular cases, including the linear one …

In this paper, we present the definitions and some properties of the general fractional
integrals (GFIs) and general fractional derivatives (GFDs) of a function f (x) with respect to …

This paper focuses on the analysis of a class of stochastic differential equations with
tempered φ-Caputo fractional derivative (φ-CFD) and Lévy noise. We propose …

Our research is primarily focused on applying the tempered (κ, ψ)-fractional operators to
investigate the existence, uniqueness, and κ-Mittag-Leffler-Ulam-Hyers stability of a specific …

In this paper, we first prove the existence, uniqueness and continuity dependence on the
initial value of multi-term Caputo tempered fractional stochastic differential equations with …

This paper deals with the controllability of fractional dynamical systems with distributed
delays modeled by Ω-Hilfer fractional derivatives. Firstly, the Ω-Hilfer fractional problem is …

In the framework of tempered fractional integrals, we obtain a fundamental identity for
differentiable convex functions. By employing this identity, we derive several modifications of …