On the solutions of fractional-time wave equation with memory effect involving operators with regular kernel

Analytical Solutions of Fractional-Order Diffusion Equations by Natural Transform Decomposition Method

“…Diffusion is the mesh movement of atoms or molecules from an area of higher concentration or great chemical potential to an area of inferior concentration or small chemical potential. In [ 13 ], the researchers generalized the classical diffusion and wave equations—different physical process such as classical diffusion, slow diffusion, the classical wave equation, and diffusion-wave hybrid. Many applications of diffusion equation, such as electrochemistry, phase transition, filtration, electromagnetism, acoustics, biochemistry, cosmology, and dynamics of biological groups [ 14 ].…”

The dynamics of a new chaotic system through the Caputo–Fabrizio and Atanagan–Baleanu fractional operators

“…Recently, a fractional logistic map and its application to dynamical analysis have been studied by Yuan et al 25 The real data application of fractional calculus to blood ethanol concentration calculation has been considered in Qureshi et al 26 The dynamics of chickenpox disease with field data is studied through fractional derivative in Qureshi and Yusuf. 27 Application of the new derivatives to the partial differential equations is considered in Yusuf et al 28 A two-strain epidemic model with fractional derivatives has been proposed in Yusuf et al 29 The application of fractional operator known as Atangana-Baleanu to Korteweg-de Vries (KDV) equation is analyzed in Inc et al 30 The dynamics of chaotic attractors with fractional conformable derivative is proposed in Pe´rez et al 31 A fractional-time wave equation with regular kernel is studied by Cuahutenango-Barro et al 32 The authors studied a fractional Hunter-Saxton equation using Riemann-Liouville and Liouville-Caputo derivatives. 33 Numerical solution of Fisher's type equations of fractional nature with Atangana-Baleanu derivative is considered in Saad et al 34 The application of Feng's first integral technique to the fractional modified Korteweg-de Vries (MKDV) equation and their analysis and solutions is presented in Ye´pez-Martnez et al 35 Motivated from the recent literature on the chaotic models, we consider a new chaotic model in two fractional operators, that is, the Caputo-Fabrizio derivative and the Atangana-Baleanu derivative, and present comparison results.…”

Some New Generalizations for Exponentially s-Convex Functions and Inequalities via Fractional Operators

“…In a fractional optimal control, either the performance index or the differential equations governing the dynamics of the system contains a term with a fractional derivative [5]. Recently, Agulilar and coauthors [6,7] and Barro et al [8] provided a new fractional operator. Fractional calculus is a terminology that refers to the integration and differentiation of an arbitrary order [1,2,9]; in other words, the meaning of k-th derivative d k y/dx k and k-th iterated integral ... dx are extended by considering a fractional α ∈ R + parameter instead of integer k ∈ N parameter.…”