Results 1 to 10 of about 358 (134)

A new generalized Hilfer-type fractional derivative with applications to space-time diffusion equation

Results in Physics, 2021
This paper is concerned to present and apply a new generalized fractional derivative, that is the Generalized Hilfer-type (GH) fractional derivative.
Tahir Ullah Khan, Muhammad Adil Khan, Yu-Ming Chu   +2 more
doaj   +3 more sources

On the (k,s)-Hilfer-Prabhakar Fractional Derivative With Applications to Mathematical Physics

Frontiers in Physics, 2020
In this paper we introduce the (k, s)-Hilfer-Prabhakar fractional derivative and discuss its properties. We find the generalized Laplace transform of this newly proposed operator. As an application, we develop the generalized fractional model of the free-
Muhammad Samraiz, Zahida Perveen, Gauhar Rahman, Kottakkaran Sooppy Nisar, Devendra Kumar   +4 more
doaj   +3 more sources

Maximum Principle for Nonlinear Fractional Differential Equations with the Hilfer Derivative

Fractal and Fractional, 2023
In this paper, two significant inequalities for the Hilfer fractional derivative of a function in the space ACγ([0,b],Rn), 0≤γ≤1 are obtained. We first verified the extremum principle for the Hilfer fractional derivative.
Abu Bakr Elbukhari, Zhenbin Fan, Gang Li
doaj   +3 more sources

Analysis of Cauchy Problems and Diffusion Equations Associated with the Hilfer–Prabhakar Fractional Derivative via Kharrat–Toma Transform

Fractal and Fractional, 2023
In this paper, the Kharrat–Toma transforms of the Prabhakar integral, a Hilfer–Prabhakar (HP) fractional derivative, and the regularized version of the HP fractional derivative are derived.
Ved Prakash Dubey, Jagdev Singh, Sarvesh Dubey, Devendra Kumar   +3 more
doaj   +3 more sources

A neural network model for managing renewable resources with population growth [PDF]

Scientific Reports
This paper presents a fractional-order modelling framework for population-resource dynamics using the $$\psi$$ -Hilfer derivative with neural network-based validation.
Sadique Ahmad, Israr Ahmad, Ala Saleh Alluhaidan, Mohammed A. ElAffendi   +3 more
doaj   +2 more sources

Hilfer Fractional Quantum Derivative and Boundary Value Problems

Mathematics, 2022
In this paper, we introduce an extension of the Hilfer fractional derivative, the “Hilfer fractional quantum derivative”, and establish some of its properties.
Phollakrit Wongsantisuk, Sotiris K. Ntouyas, Donny Passary, Jessada Tariboon   +3 more
doaj   +1 more source

Existence Results for Hilfer Fractional Differential Equations with Variable Coefficient

Fractal and Fractional, 2021
The aim of this paper is to establish the existence and uniqueness results for differential equations of Hilfer-type fractional order with variable coefficient.
Fang Li, Chenglong Wang, Huiwen Wang
doaj   +1 more source

On Hilfer generalized proportional fractional derivative

Advances in Difference Equations, 2020
Motivated by the Hilfer and the Hilfer–Katugampola fractional derivative, we introduce in this paper a new Hilfer generalized proportional fractional derivative, which unifies the Riemann–Liouville and Caputo generalized proportional fractional ...
Idris Ahmed, Poom Kumam, Fahd Jarad, Piyachat Borisut, Wachirapong Jirakitpuwapat   +4 more
doaj   +1 more source

Infinite Interval Problems for Fractional Evolution Equations

Mathematics, 2022
In this paper, we investigate infinite interval problems for the fractional evolution equations with Hilfer fractional derivative. By using the generalized Ascoli–Arzelà theorem and some new techniques, we prove the existence of mild solutions of Hilfer ...
Yong Zhou
doaj   +1 more source

A Survey on Recent Results on Lyapunov-Type Inequalities for Fractional Differential Equations

Fractal and Fractional, 2022
This survey paper is concerned with some of the most recent results on Lyapunov-type inequalities for fractional boundary value problems involving a variety of fractional derivative operators and boundary conditions.
Sotiris K. Ntouyas, Bashir Ahmad, Jessada Tariboon   +2 more
doaj   +1 more source