Collocation methods for fractional differential equations involving non-singular kernel

By Dumitru Băleanu, Babak Shiri. Chaos, Solitons & Fractals, 2018

102 citations recorded by the source corpus.

Abstract A system of fractional differential equations involving non-singular Mittag-Leffler kernel is considered. This system is transformed to a type of weakly singular integral equations in which the weak singular kernel is involved with both the unknown and known functions. The regularity and existence of its solution is studied. The collocation methods on discontinuous piecewise polynomial space are considered. The convergence and superconvergence properties of the introduced methods are derived on graded meshes. Numerical results provided to show that our theoretical convergence bounds are often sharp and the introduced methods are efficient. Some comparisons and applications are discussed.

Subfields: Mechanics of Materials, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/b008bfa46ecee752a69421b037e1d6834ef060da

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In Mechanics of Materials

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Integral inequalities for a fractional operator of a function with respect to another function with nonsingular kernel (2020, background): “After Leibniz, many famous mathematicians and physicians have studied theory and application of this model for fractional derivatives and integrals and fractional differential equations; see for detail [12, 13, 35, 55].”
On the solution of time‐fractional dynamical model of Brusselator reaction‐diffusion system arising in chemical reactions (2020, methodology): “Consider the following fractional Brusselator reaction-diffusion system (BRDS)29,31: Dαt ψ =ψ 2ξ− A+1ð Þψ + μ ∂ 2ψ ∂x2 + ∂2ψ ∂y2 +B, Dβt ξ= −ψ2ξ+Aψ + μ ∂ξ2 ∂x2 + ∂ξ2 ∂y2 , 8>>< >>: ð15Þ with ICs 19,24 ψ x,y,0ð Þ= e− x+ yð Þ, ξ x,y,0ð Þ= e x+ yð Þ: ( ð16Þ Applying FRDTM to Equation (15) with ICs (Equ”
Spline collocation methods for seismic analysis of multiple degree of freedom systems with visco-elastic dampers using fractional models (2020, methodology): “One of the classical methods for solving integral or differential equations is the collocation method on piecewise polynomial spaces which is known as the spline collocation method (Baleanu and Shiri, 2018; Brunner, 2004; Shiri, 2014; Shiri and Baleanu, 2019).”