Results 41 to 50 of about 3,290 (179)

Optimal error estimate of the Legendre spectral approximation for space-fractional reaction–advection–diffusion equation

Advances in Difference Equations, 2018
In this paper, we consider the space-fractional reaction–advection–diffusion equation with fractional diffusion and integer advection terms. By treating the first-order integer derivative as the composition of two Riemann–Liouville fractional derivative ...
Wenping Chen, Shujuan Lü, Hu Chen, Haiyu Liu   +3 more
doaj   +1 more source

Exponential Stability of Higher Order Fractional Neutral Stochastic Differential Equation Via Integral Contractors

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6425-6446, April 2025.
ABSTRACT The well‐posedness results for mild solutions to the fractional neutral stochastic differential system with Rosenblatt process with Hurst index Ĥ∈12,1$$ \hat{H}\in \left(\frac{1}{2},1\right) $$ is discussed in this article. To demonstrate the results, the concept of bounded integral contractors is combined with the stochastic result and ...
Dimplekumar N. Chalishajar, Dhanalakshmi Kasinathan, Ramkumar Kasinathan, Ravikumar Kasinathan   +3 more
wiley   +1 more source

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

Fractional Integral Inequalities of Riemann–Liouville Type for Higher‐Order Differentiable Convex Mappings

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In this paper, we investigate several Riemann–Liouville fractional integral inequalities for higher‐order differentiable functions using a simple and novel approach. First, we present an inequality involving fractional integrals that generalizes the right‐hand side of the fundamental Hermite–Hadamard inequality to higher‐order derivatives ...
Samet Erden, Hüseyin Budak
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

Finite Biorthogonal Polynomials Suggested by the Finite Orthogonal Polynomials Mnp,qx$$ {M}_n^{\left(p,q\right)}(x) $$

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Constructing a biorthogonal structure from scratch, that is, defining a biorthogonal pair is quite tough. Because here the orthogonality must be established between two different sets. There are four known univariate biorthogonal polynomial sets, suggested by Laguerre, Jacobi, Hermite and Szegő‐Hermite polynomials, in the literature.
Esra Güldoğan Lekesiz
wiley   +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