A Multiscale Fractal Approach for Determining Cushioning Curves of Low-Density Polymer Foams by Mariela C. Bravo-Sánchez, Luis M. Palacios-Pineda, José L. Gómez-Color, Oscar Martínez-Romero, Imperio A. Perales-Martínez, Daniel Olvera-Trejo, Jorge A. Estrada-Díaz, Alex Elías-Zúñiga

“…To capture the multiscale nature of the dynamic response behavior of two low-density foams to sustain impact loads, fractional differential equations of motion are used to qualitatively and quantitatively describe the dynamic response behavior, assuming restoring forces for each foam characterized, respectively, by a polynomial of heptic degree and by a trigonometric tangential function. …”
Get full text

Analyzing crop production: Unraveling the impact of pests and pesticides through a fractional model by Navnit Jha, Akash Yadav, Ritesh Pandey, A.K. Misra

“…The feasibility of every possible nonnegative equilibrium and its stability characteristics are explored utilizing the stability theory of fractional differential equations. Our model analysis reveals that in a continuous spray approach, the roles of pesticide abatement rate and pesticide uptake rate can be interchanged. …”
Get full text

Positive Solutions Depending on Parameters for a Nonlinear Fractional System with p-Laplacian Operators by Chen Yang, Xiaolin Zhu

“…This paper considers a system of fractional differential equations involving p-Laplacian operators and two parameters D0+α1φp1D0+β1ut+λft,ut,vt=0,0<t<1,D0+α2φp2D0+β2vt+μgt,ut,vt=0,0<t<1,u0=u1=u′0=u′1=0,D0+β1u0=0,D0+β1u1=b1D0+β1uη1,v0=v1=v′0=v′1=0,D0+β2v0=0,D0+β2v1=b2D0+β2vη2, where αi∈1,2, βi∈3,4, D0+αi and D0+βi are the standard Riemann-Liouville derivatives, φpis=spi−2s,pi>1, φpi−1=φqi, 1/pi+1/qi=1,ηi∈0,1,bi∈0,ηi1−αi/pi−1, i=1,2, and f,g∈C0,1×0,+∞×0,+∞,0,+∞ and λ and μ are two positive parameters. …”
Get full text

Advanced Fractional Mathematics, Fractional Calculus, Algorithms and Artificial Intelligence with Applications in Complex Chaotic Systems by Dumitru Baleanu, Yeliz Karaca

“…Thus, fields with a broad range of spectrum range from mathematics, physics, biology, fluid mechanics, medicine, engineering, image analysis, based on differing perspectives in our special issue which presents a compilation of recent research elaborating on the related advances in foundations, theory, methodology and topic-based implementations regarding fractals, fractal methodology, fractal spline, non-differentiable fractal functions, fractional calculus, fractional mathematics, fractional differential equations, differential equations (PDEs, ODEs), chaos, bifurcation, Lie symmetry, stability, sensitivity, deep learning approaches, machine learning, and so forth through advanced fractional mathematics, fractional calculus, data intensive schemes, algorithms and machine learning applications surrounding complex chaotic systems.…”
Get full text