Results 51 to 60 of about 38,304 (201)

Refinements of some fractional integral inequalities involving extended convex functions and fractional Caputo derivatives

Journal of Inequalities and Applications
This article examines famous fractional Hermite–Hadamard integral inequalities through the applications of fractional Caputo derivatives and extended convex functions. We develop modifications involving two known classical fractional extended versions of
Muhammad Imran, Shahid Mubeen, Aziz Khan, Thabet Abdeljawad   +3 more
doaj   +1 more source

The Variable-Order Fractional Calculus of Variations

, 2018
This book intends to deepen the study of the fractional calculus, giving special emphasis to variable-order operators. It is organized in two parts, as follows. In the first part, we review the basic concepts of fractional calculus (Chapter 1) and of the
Almeida, Ricardo, Tavares, Dina, Torres, Delfim F. M.   +2 more
core   +1 more source

Blowing‐Up Solution of a System of Fractional Differential Equations With Variable Order

Mathematical Methods in the Applied Sciences, Volume 48, Issue 9, Page 9726-9743, June 2025.
ABSTRACT We investigated the necessary condition for blowing‐up solutions in finite time of the system u′(t)+(1)D0|tα(t)(u(t)−u0)=|v(t)|q,t>0,q>1,v′(t)+(1)D0|tβ(t)(v(t)−v0)=|u(t)|p,t>0,p>1$$ {u}^{\prime }(t)+{}_{(1)}{D}_{0\mid t}^{\alpha (t)}\left(u(t)-{u}_0\right)={\left|v(t)\right|}^q,\kern0.3em t>0,q>1,{v}^{\prime }(t)+{}_{(1)}{D}_{0\mid t}^{\beta ...
Muhammad Rizki Fadillah, Mokhtar Kirane
wiley   +1 more source

Stability analysis of solutions and existence theory of fractional Lagevin equation

Alexandria Engineering Journal, 2021
The present article describes fractional Langevin equations (FDEs) invloving Caputo Hadamard-derivative of independent orders connected with non-local integral and non-periodic boundary conditions.
Amita Devi, Anoop Kumar, Thabet Abdeljawad, Aziz Khan   +3 more
doaj   +1 more source

Recovering discrete delayed fractional equations from trajectories

Mathematical Methods in the Applied Sciences, Volume 48, Issue 7, Page 7630-7640, 15 May 2025.
We show how machine learning methods can unveil the fractional and delayed nature of discrete dynamical systems. In particular, we study the case of the fractional delayed logistic map. We show that given a trajectory, we can detect if it has some delay effect or not and also to characterize the fractional component of the underlying generation model.
J. Alberto Conejero, Òscar Garibo‐i‐Orts, Carlos Lizama   +2 more
wiley   +1 more source

Galerkin Finite Element Method for Caputo–Hadamard Time-Space Fractional Diffusion Equation

Mathematics
In this paper, we study the Caputo–Hadamard time-space fractional diffusion equation, where the Caputo derivative is defined in the temporal direction and the Hadamard derivative is defined in the spatial direction separately.
Zhengang Zhao, Yunying Zheng
doaj   +1 more source

Existence and Uniqueness Results for the Coupled Pantograph System With Caputo Fractional Operator and Hadamard Integral

International Journal of Differential Equations, Volume 2025, Issue 1, 2025.
The main objective of this research involves studying a new novel coupled pantograph system with fractional operators together with nonlocal antiperiodic integral boundary conditions. The system consists of nonlinear pantograph fractional equations which integrate with Caputo fractional operators and Hadamard integrals.
Gunaseelan Mani, Vasu Lakshmanan, Abdul Razak Kachu Mohideen, Homan Emadifar, Patricia J. Y. Wong   +4 more
wiley   +1 more source

Survey and new results on boundary-value problems of singular fractional differential equations with impulse effects

Electronic Journal of Differential Equations, 2016
Firstly we prove existence and uniqueness of solutions of Cauchy problems of linear fractional differential equations (LFDEs) with two variable coefficients involving Caputo fractional derivative, Riemann-Liouville derivative, Caputo type Hadamard ...
Yuji Liu
doaj  

Jacobi polynomials method for a coupled system of Hadamard fractional Klein–Gordon–Schrödinger equations

Alexandria Engineering Journal
In this work, the Caputo-type Hadamard fractional derivative is utilized to introduce a coupled system of time fractional Klein–Gordon-Schrödinger equations.
M.H. Heydari, M. Razzaghi
doaj   +1 more source

An Infinite System of Fractional Order with p-Laplacian Operator in a Tempered Sequence Space via Measure of Noncompactness Technique

Fractal and Fractional, 2021
In the current study, a new class of an infinite system of two distinct fractional orders with p-Laplacian operator is presented. Our mathematical model is introduced with the Caputo–Katugampola fractional derivative which is considered a generalization ...
Ahmed Salem, Lamya Almaghamsi, Faris Alzahrani   +2 more
doaj   +1 more source