Results 21 to 30 of about 1,380 (204)

Applications of Fixed Point Theory to Investigate a System of Fractional Order Differential Equations

Journal of Function Spaces, 2021
We investigate a nonlinear system of pantograph-type fractional differential equations (FDEs) via Caputo-Hadamard derivative (CHD). We establish the conditions for existence theory and Ulam-Hyers-type stability for the underlying boundary value system ...
Zareen A. Khan, Israr Ahmad, Kamal Shah
doaj   +1 more source

A note on Hadamard fractional differential equations with varying coefficients and their applications in probability

, 2017
In this paper we show several connections between special functions arising from generalized COM-Poisson-type statistical distributions and integro-differential equations with varying coefficients involving Hadamard-type operators. New analytical results
Garra, Roberto, Orsingher, Enzo, Polito, Federico   +2 more
core   +1 more source

New study on Caputo-Hadamard type fractional Neutral Integro-Differential equations [PDF]

Mathematics and Computational Sciences
In this work, we focus on the analysis of fractional-order neutral integro-differential equations using the Caputo-Hadamard fractional derivative. We employed the topological degree method (TDM) to derive results and solutions for these equations.
Emimal Navajothi, Selvi Sellappan
doaj   +1 more source

New Fractional Integral Inequalities for Convex Functions Pertaining to Caputo–Fabrizio Operator

Fractal and Fractional, 2022
In this article, a generalized midpoint-type Hermite–Hadamard inequality and Pachpatte-type inequality via a new fractional integral operator associated with the Caputo–Fabrizio derivative are presented.
Soubhagya Kumar Sahoo, Pshtiwan Othman Mohammed, Bibhakar Kodamasingh, Muhammad Tariq, Y. S. Hamed   +4 more
doaj   +1 more source

Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations

, 2018
In this paper we obtain new estimates of the Hadamard fractional derivatives of a function at its extreme points. The extremum principle is then applied to show that the initial-boundary-value problem for linear and nonlinear time-fractional diffusion ...
Kirane, Mokhtar, Torebek, Berikbol T.
core   +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

Lyapunov Direct Method for Nonlinear Hadamard-Type Fractional Order Systems

Fractal and Fractional, 2022
In this paper, a rigorous Lyapunov direct method (LDM) is proposed to analyze the stability of fractional non-linear systems involving Hadamard or Caputo–Hadamard derivatives.
Changping Dai, Weiyuan Ma
doaj   +1 more source

A generalization of the Lomnitz logarithmic creep law via Hadamard fractional calculus

, 2017
We present a new approach based on linear integro-differential operators with logarithmic kernel related to the Hadamard fractional calculus in order to generalize, by a parameter $\nu \in (0,1]$, the logarithmic creep law known in rheology as Lomnitz ...
Garra, Roberto, Mainardi, Francesco, Spada, Giorgio   +2 more
core   +1 more source

A local discontinuous Galerkin method for the Caputo–Hadamard Burgers equation: Analysis and parameter estimation [PDF]

AIP Advances
This paper develops and analyzes a fully discrete numerical scheme for the time-fractional Burgers equation with a Caputo–Hadamard derivative, which incorporates a logarithmic kernel particularly suitable for modeling ultraslow diffusion processes.
Zhen Wang, Xiaoting Li
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