Results 71 to 80 of about 2,558 (225)

Extended Jacobi Functions via Riemann-Liouville Fractional Derivative [PDF]

Abstract and Applied Analysis, 2013
By means of the Riemann-Liouville fractional calculus, extended Jacobi functions are de…fined and some of their properties are obtained. Then, we compare some properties of the extended Jacobi functions extended Jacobi polynomials. Also, we derive fractional differential equation of generalized extended Jacobi functions.
Bayram Çekim, Esra Erkuş-Duman
openaire   +4 more sources

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  

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

SOLVABILITY OF THE CAUCHY PROBLEM FOR EQUATIONS WITH RIEMANN–LIOUVILLE’S FRACTIONAL DERIVATIVES

Doklady of the National Academy of Sciences of Belarus, 2018
In this article we study the solvability of the analogue of the Cauchy problem for ordinary differential equations with Riemann–Liouville’s fractional derivatives with a nonlinear restriction on the right-hand side of functions in certain spaces. The conditions for solvability of the problem under consideration in given function spaces, as well as the ...
Zabreĭko, Petr Petrovich, Ponomareva, Svetlana Vladimirovna   +1 more
openaire   +3 more sources

Boundary-value problems for differential inclusions with Riemann–Liouville fractional derivative [PDF]

Nonlinear Oscillations, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Benchohra, M., Djebali, S., Hamani, S.
openaire   +2 more sources

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

Study on the variable coefficient space–time fractional Korteweg de Vries equation

Ain Shams Engineering Journal, 2018
In this paper, the fractional Riccati method is modified for solving nonlinear variable coefficients fractional differential equations involving modified Riemann–Liouville derivative.
Emad A-B. Abdel-Salam, Gamal F. Hassan
doaj   +1 more source

Some aspects of the numerical analysis of a fractional duffing oscillator with a fractional variable order derivative of the Riemann-Liouville type [PDF]

, 2022
V. A. Kim, Roman Parovik
openalex   +1 more source

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

Numerical Algorithms for the Fractional Diffusion-Wave Equation with Reaction Term

Abstract and Applied Analysis, 2013
Two numerical algorithms are derived to compute the fractional diffusion-wave equation with a reaction term. Firstly, using the relations between Caputo and Riemann-Liouville derivatives, we get two equivalent forms of the original equation, where we ...
Hengfei Ding, Changpin Li
doaj   +1 more source