Advances in solving conformable nonlinear partial differential equations and new exact wave solutions for Oskolkov‐type equations

Abstract

This paper introduces advances in solving space‐time conformable nonlinear partial differential equations (PDEs) and exact wave solutions for Oskolkov equations. To arrive at these advances, nonlinear PDEs with space and time conformable partial derivatives are reduced to differential equations with conformable derivatives by using new modifications of the exponential rational function method (ERFM). These modifications are efficious approaches for obtaining exact analytical solutions. An important result of this work is that it yields new exact wave solutions for space‐time conformable pseudo‐parabolic type equations. The graphical representations of the obtained solutions are shown to confirm the accuracy and efficiency of the suggested method.

Conformable mathematical modeling of the COVID‐19 transmission dynamics: A more general study

“…The graphs for the susceptible population s 1 (x, t) in system (33) for 𝛼 = 0.5 (on the left) and 𝛼 = 1 (on the right). It is expected to have more cases in the susceptible population when the time increases during the pandemic.…”

“…The graphs for the infected population i 1 (x, t) in system (33) for 𝛼 = 0.5 (on the left) and 𝛼 = 1 (on the right). We see that number of cases slowly increases during the pandemic time.…”

“…One of the most powerful methods for obtaining an exact solution is the exponential rational function method (ERFM). The ERFM has been widely used to obtain a series of exact solutions for higher dimensional nonlinear PDEs; see, for example, Ghanbari et al [29] introduced exact solutions of Biswas-Milovic equation by an ERFM, Ghanbari et al [30] introduced a generalized ERFM for extended Zakharov-Kuzetsov equation with conformable derivative, Kumar et al [31] obtained exact solitary wave solutions of the strain wave equation in microstructured solids via the generalized ERFM, Mohyud-Din and Bibi [32] obtained exact solutions for nonlinear fractional differential equations using the ERFM, and Thabet et al [33] introduced advances of ERFM and exact solutions of conformable PDEs.…”

Fractional mathematical modeling for the transmission dynamics of SARS-CoV-2 infection

“…Fractional PDEs which involve fractional partial derivatives, in time or/and space, have been considered in many ways as a novel topic and they have been the subjects of several conferences due to their important applications in natural and applied sciences. [1][2][3][4][5][6][7][8][9][10][11]. Several problems in biology, ecology, ontology, and epidemiology need to be modeled in terms of fractional PDEs through mathematical modeling.…”

Sıkıştırılamaz Visko Elastik Kelvin-Voigt Sıvısında Ortaya Çıkan Oskolkov Denkleminin Gezici Dalga Çözümleri

“…The Oskolkov equation appears in various studies such as different types of traveling wave solutions of the Oskolkov equation have been investigated using the modified ( / ) GG  -expansion method [1], Ghanbari has been presented exact solutions for two Oskolkov-type equations [22], exact solutions have been attained for the Oskolkov equation [23], Thabet et al have been presented exact solutions for Oskolkov equations with exponential rational function method [24], Gozukızıl and Akcagıl have been created the exact solutions for the Oskolkov equation via tanh-coth method [25].…”