Results 81 to 90 of about 602,498 (123)

Cauchy problem for fractional evolution equations with Caputo derivative

, 2013
This paper concerns the abstract nonlocal Cauchy problem of a class of fractional evolution equations with Caputo derivative. A suitable mild solution of evolution equations with Caputo derivative is introduced.
X.H. Shen, L. Zhang, Y. Zhou
core   +1 more source

Impulsive Fractional Differential Inclusions Involving the Caputo Fractional Derivative [PDF]

, 2009
In this paper, we establish sufficient conditions for the existence of solutions for a class of initial value problem for impulsive fractional differential inclusions involving the Caputo fractional derivative. Both cases of convex and nonconvex valued
Hamani, S., Benchohra, M., Ait Dads, E.
core   +1 more source

Analysis of Tumor‐Immune Dynamics With T Cells and Dendritic Cells Using Fractional Extension of He‐Laplace Framework

Engineering Reports, Volume 8, Issue 11, November 2026.
Computational modeling of tumors is foundational in exploring cancer behavior, guiding clinical decision‐making, and assessing therapeutic impact in a controlled, predictive framework. While integer‐order models have been extensively explored in the past, innovative applications of fractional calculus to cancer‐immune system modeling remain largely ...
Mubashir Qayyum, Sidra Nayab, Saraswati Acharya   +2 more
wiley   +1 more source

Homotopy Perturbation ρ-Laplace Transform Method and Its Application to the Fractional Diffusion Equation and the Fractional Diffusion-Reaction Equation

Fractal and Fractional, 2019
In this paper, the approximate solutions of the fractional diffusion equations described by the fractional derivative operator were investigated. The homotopy perturbation Laplace transform method of getting the approximate solution was proposed.
Ndolane Sene, Aliou Niang Fall
doaj   +1 more source

Existence of Solutions for Anti-Periodic Fractional Differential Inclusions Involving ψ-Riesz-Caputo Fractional Derivative

, 2019
In this paper, we investigate the existence of solutions for a class of anti-periodic fractional differential inclusions with ψ -Riesz-Caputo fractional derivative.
Chuanzhi Bai, Dandan Yang
core   +1 more source

Calculus of variations involving Caputo-Fabrizio fractional differentiation [PDF]

, 2018
This paper is devoted to study some variational problems with functionals containing the Caputo-Fabrizio fractional derivative, that is a fractional derivative with a non-singular ...
Bastos, Nuno R. O., Nuno R. O. Bastos
core   +1 more source

A New Mixed Fractional Derivative with Applications in Computational Biology

Computation
This study develops a new definition of a fractional derivative that mixes the definitions of fractional derivatives with singular and non-singular kernels.
Khalid Hattaf
doaj   +1 more source

High Order Approximation to Caputo Derivative On Graded Mesh and Time-Fractional Diffusion Equation for Non-smooth Solutions

In this paper, a high-order approximation to Caputo-type time-fractional diffusion equations involving an initial-time singularity of the solution is proposed.
Kumari, Shweta, Singh, Abhishek Kumar, Mehandiratta, Vaibhav, Mehra, Mani   +3 more
core   +1 more source

Generalized caputo fractional derivative and its applications

, 2012
Özarslan ve Özergin 2010 yılında yayınladıkları bir makalelerinde [1], orijinal Riemann-Liouville kesirli türev operatörüne ekstra bir parametre ekleyerek operatörü genisletmislerdir.
Sökmen, Yusuf
core  

Numerical methods for fractional differential equations by new caputo and hadamard types operators [PDF]

, 2020
Fractional ordinary differential equation (FODE) and fractional partial differential equation (FPDE) emerges in various modelling of physics phenomena. Over past decades, several fractional derivative and operator has been introduced such as Caputo-
Toh, Yoke Teng
core   +1 more source