Results 31 to 40 of about 1,833 (139)

Riemann–Liouville Fractional Calculus of Nonlinear Hidden Variable Recurrent Fractal Interpolation Functions Based on Rakotch Contraction

Journal of Function Spaces
In this paper, we study Riemann–Liouville fractional calculus of nonlinear hidden variable recurrent fractal interpolation function (HVRFIF) constructed based on Rakotch contraction, which is a generalization of Banach contraction.
Chung-Il Ro, Chol-Hui Yun, Song-Chol Kwon, Un-Ryong Rim   +3 more
doaj   +1 more source

Solving General Differential Equations of Fractional Orders Via Rohit Transform [PDF]

Kirkuk Journal of Science
inspecting the attributes of derivatives and integrals of fractional orders known as fractional derivatives and integrals. In this article, a far-out complex integral transform known as the Rohit transform (RT) is put into use for working out general ...
Rohit Gupta, Rahul Gupta, Dinesh Verma
doaj   +1 more source

Left Riemann–Liouville Fractional Sobolev Space on Time Scales and Its Application to a Fractional Boundary Value Problem on Time Scales

Fractal and Fractional, 2022
First, we show the equivalence of two definitions of the left Riemann–Liouville fractional integral on time scales. Then, we establish and characterize fractional Sobolev space with the help of the notion of left Riemann–Liouville fractional derivative ...
Xing Hu, Yongkun Li
doaj   +1 more source

Equivalences of Nonlinear Higher Order Fractional Differential Equations With Integral Equations

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6930-6942, April 2025.
ABSTRACT Equivalences of initial value problems (IVPs) of both nonlinear higher order (Riemann–Liouville type) fractional differential equations (FDEs) and Caputo FDEs with the corresponding integral equations are studied in this paper. It is proved that the nonlinearities in the FDEs can be L1$$ {L}^1 $$‐Carathéodory with suitable conditions.
Kunquan Lan
wiley   +1 more source

Riemann–Liouville Type Fractional Derivatives and Equivalences of Linear Riemann–Liouville Type Fractional Differential Equations

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT The first or higher order Riemann–Liouville (R‐L) type fractional derivatives are studied. The relations between the R‐L type fractional derivatives and the classical R‐L fractional derivatives are obtained and the spaces of functions on which the R‐L type fractional derivatives exist are provided.
Kunquan Lan
wiley   +1 more source

A Simple and Effective Second-Order Numerical Algorithm for Tempered Fractional Differential Equation With Time Caputo-Tempered Fractional Derivative

Advances in Mathematical Physics
This paper presents an efficient numerical scheme for the space–time tempered fractional convection–diffusion equation, where the time derivative is the Caputo-tempered fractional derivative and the space derivatives are the normalized left and right ...
Dechao Gao, Zeshan Qiu, Lizan Wang, Jianxin Li   +3 more
doaj   +1 more source

On the Solutions Fractional Riccati Differential Equation with Modified Riemann-Liouville Derivative

International Journal of Differential Equations, 2012
Fractional variational iteration method (FVIM) is performed to give an approximate analytical solution of nonlinear fractional Riccati differential equation. Fractional derivatives are described in the Riemann-Liouville derivative.
Mehmet Merdan
doaj   +1 more source

A New Generalized Definition of Fractional Derivative with Non-Singular Kernel

Computation, 2020
This paper proposes a new definition of fractional derivative with non-singular kernel in the sense of Caputo which generalizes various forms existing in the literature. Furthermore, the version in the sense of Riemann–Liouville is defined.
Khalid Hattaf
doaj   +1 more source

Sliding Mode Control in Aerospace Applications: A Survey

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT Sliding mode control (SMC) enjoys robustness to matched and unmatched (in the case of minimum phase input‐output dynamics) bounded perturbations, and finite time convergence. Second‐order and higher‐order sliding mode control systems (2‐SMC/HOSMC) retain all the advantages of sliding mode control, but in addition can be applied to systems of ...
Yuri Shtessel, Christopher Edwards
wiley   +1 more source

On the Hermite–Hadamard type inequality for ψ-Riemann–Liouville fractional integrals via convex functions

Journal of Inequalities and Applications, 2019
In this paper, we establish a new Hermite–Hadamard inequality involving left-sided and right-sided ψ-Riemann–Liouville fractional integrals via convex functions.
Kui Liu, JinRong Wang, Donal O’Regan
doaj   +1 more source