Results 71 to 80 of about 3,290 (179)

A New Gronwall–Bellman Inequality in Frame of Generalized Proportional Fractional Derivative

Mathematics, 2019
New versions of a Gronwall−Bellman inequality in the frame of the generalized (Riemann−Liouville and Caputo) proportional fractional derivative are provided.
Jehad Alzabut, Weerawat Sudsutad, Zeynep Kayar, Hamid Baghani   +3 more
doaj   +1 more source

Matsumura‐Type Estimates and Global Solutions of a Fractional Wave Equation With Nonlocal Nonlinearity

Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 9967-9983, June 2026.
ABSTRACT The main results of this paper are the global existence and long time behavior of solutions of a fractional wave equation with a nonlocal nonlinearity. The techniques in this work rely on norm estimates of the solutions of εutt+ut+(−Δ)βu=0,u(0,x)=φ(x),ut(0,x)=ψ(x),$$ \varepsilon {u}_{tt}+{u}_t+{\left(-\Delta \right)}^{\beta }u=0,\kern1em u ...
Ibrahim Ahmad Suleman, Mokhtar Kirane
wiley   +1 more source

Improvement on Conformable Fractional Derivative and Its Applications in Fractional Differential Equations

Journal of Function Spaces, 2020
In this paper, we made improvement on the conformable fractional derivative. Compared to the original one, the improved conformable fractional derivative can be a better replacement of the classical Riemann-Liouville and Caputo fractional derivative in ...
Feng Gao, Chunmei Chi
doaj   +1 more source

A Numerical Method Combining Cubic Interpolated Propagation and Shifted Grünwald–Letnikov for Fractional Advection–Dispersion Equations

International Journal for Numerical and Analytical Methods in Geomechanics, Volume 50, Issue 8, Page 3546-3557, 10 June 2026.
ABSTRACT Recent advances in the numerical solution of fractional partial differential equations have yielded promising results. In particular, the Shifted Grünwald–Letnikov (SGL) approach allows for a generalization of the traditional finite difference method to the context of fractional differential equations.
Pedro Victor Serra Mascarenhas, André Luís Brasil Cavalcante   +1 more
wiley   +1 more source

On the Approximate Controllability of Fractional Evolution Equations with Generalized Riemann-Liouville Fractional Derivative

, 2015
We discuss the approximate controllability of fractional evolution equations involving generalized Riemann-Liouville fractional derivative. The results are obtained with the help of the theory of fractional calculus, semigroup theory, and the Schauder ...
N. I. Mahmudov, M. A. McKibben
core   +1 more source

Oscillation of solutions to nonlinear forced fractional differential equations

Electronic Journal of Differential Equations, 2013
In this article, we study the oscillation of solutions to a nonlinear forced fractional differential equation. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative.
Qinghua Feng, Fanwei Meng
doaj  

Capturing Complex Rate‐Dependent Behaviors of Saturated Clays: A Fractional Consistency Kinematic Hardening Viscoplastic Approach

International Journal for Numerical and Analytical Methods in Geomechanics, Volume 50, Issue 8, Page 3281-3296, 10 June 2026.
ABSTRACT Saturated high plasticity clays show complex nonlinear, rate‐dependent, and hysteresis behaviors under non‐monotonic stress paths, requiring advanced mathematical constitutive equations for accurate description. Taking into account the inherent advantages of kinematic hardening mechanisms in simulating complex stress histories, this paper ...
Wei Cheng, Zhen‐Yu Yin
wiley   +1 more source

Fractional-order boundary value problem with Sturm-Liouville boundary conditions

Electronic Journal of Differential Equations, 2015
Using the new conformable fractional derivative, which differs from the Riemann-Liouville and Caputo fractional derivatives, we reformulate the second-order conjugate boundary value problem in this new setting.
Douglas R. Anderson, Richard I. Avery
doaj  

Integrating Experimental Imaging and (Quantum‐Deformation)‐Curvature Dynamics in Bleb Morphogenesis

Engineering Reports, Volume 8, Issue 4, April 2026.
We propose a (q,τ)$$ \left(q,\tau \right) $$‐fractional geometric flow model for cell blebbing that incorporates hereditary memory and viscoelastic effects in curvature‐driven membrane dynamics. Image‐based measurements of bleb geometry are coupled with fractional evolution equations and validated numerically.
Rabha W. Ibrahim, Dumitru Baleanu, Soheil Salahshour   +2 more
wiley   +1 more source

Impulsive periodic boundary value problems for fractional differential equation involving Riemann–Liouville sequential fractional derivative

, 2011
In this paper, we investigate the existence of solutions of the periodic boundary value problem for nonlinear impulsive fractional differential equation involving Riemann–Liouville sequential fractional derivative by using monotone iterative method.
Bai, Chuanzhi, Chuanzhi Bai
core   +1 more source