Results 91 to 100 of about 12,737 (208)

A comment on some new definitions of fractional derivative

, 2018
After reviewing the definition of two differential operators which have been recently introduced by Caputo and Fabrizio and, separately, by Atangana and Baleanu, we present an argument for which these two integro-differential operators can be understood ...
Giusti, Andrea
core   +1 more source

Generalizations of Riemann–Liouville fractional integrals and applications

Mathematical Methods in the Applied Sciences
The notion of a generalized Riemann–Liouville fractional integral is introduced, and its domain, range, and properties are studied. The new notion and properties provide new insight and understanding into the classical Riemann–Liouville fractional integral and its properties.
openaire   +1 more source

On Fractional Integral Inequalities Involving Riemann-Liouville Operators

, 2022
Here, we seek to prove some novel fractional integral inequalities for synchronous functions connected to the Chebyshev functional, involving the Gauss hypergeometric function. The final section presents a number of special instances as fractional integral inequalities involving Riemann-Liouville type fractional integral operators.
Kalpana Rajput,, Rajshreemishra,, D.K. Jain,, Farooq Ahmad,, Peer Javaid Ahmad,   +4 more
openaire   +1 more source

Neuronal Dynamics of an Intrinsically Bursting Neuron Through the Caputo–Fabrizio Fractal–Fractional Hodgkin–Huxley Model

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This study introduces a novel fractal–fractional extension of the Hodgkin–Huxley model to capture complex neuronal dynamics, with particular focus on intrinsically bursting patterns. The key innovation lies in the simultaneous incorporation of Caputo–Fabrizio operators with fractional order α for memory effects and fractal dimension τ for temporal ...
M. J. Islam, M. J. Abedin, A. Hoque, M. G. Hafez, Jaume Giné   +4 more
wiley   +1 more source

The Essential Gronwall Inequality Demands the $\left(\rho,\varphi \right) -$Fractional Operator with Applications in Economic Studies

Universal Journal of Mathematics and Applications
Gronwall's inequalities are important in the study of differential equations and integral inequalities. Gronwall inequalities are a valuable mathematical technique with several applications.
Rabha Ibrahim, Zoubir Dahmani, Mohamed Bezzıou   +2 more
doaj   +1 more source

A Lucas Operational Matrix Method for Solving Nonlinear Fractional Two‐Dimensional Partial Volterra Integral Equations

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
This paper introduces a new numerical method for solving a class of two‐dimensional fractional partial Volterra integral equations (2DFPVIEs). Our approach uses Lucas polynomials (LPs) to construct operational matrices (OMs) that effectively transform the complex fractional‐order equations into a more manageable system of algebraic equations.
S. S. Gholami, A. Ebadian, A. A. Khajehnasiri, Kareem T. Elgindy, Birendra Nath Mandal   +4 more
wiley   +1 more source

Hermite-Hadamard type inequalities, convex stochastic processes and Katugampola fractional integral

Revista Integración, 2018
In this work we present some Hermite-Hadamard type inequalities for convex Stochastic Processes using the Katugampola fractional integral, and from these results specific cases are deduced for the Riemann-Liouville fractional integral and Riemann ...
Jorge E. Hernández H., Juan Francisco Gómez   +1 more
doaj  

Comparison of Integer‐, Constant‐, and Variable‐Order Fractional Models of Competition for Student Population Using Caputo–Fabrizio Fractional Derivative With Policy Interventions

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
This study develops constant‐order (CO) and variable‐order (VO) Caputo–Fabrizio (CF) fractional derivative (CFFD) models to extend the classical integer‐order framework for analyzing competition among public, private, and nonenrolled student populations under varying policy intervention intensities.
Kiprotich Ezra Bett, Cyrus Gitonga Ngari, Grace Gakii Muthuri, Kareem Elgindy   +3 more
wiley   +1 more source

Riemann–Liouville Operator in Weighted L_p Spaces via the Jacobi Series Expansion

Axioms, 2019
In this paper, we use the orthogonal system of the Jacobi polynomials as a tool to study the Riemann−Liouville fractional integral and derivative operators on a compact of the real axis.
Maksim V. Kukushkin
doaj   +1 more source

General (k, p)-Riemann-Liouville fractional integrals

Filomat
The main motivation of this study is to establish a general version of the Riemann-Liouville fractional integrals with two exponential parameters k and p which is determined over the (k, p)-gamma function. In particular, we present the harmonic, geometric and arithmetic (k, p)-Riemann-Liouville frac-tional integrals.
Budak, HÜSEYİN, Benaissa, Bouharket
openaire   +2 more sources