Two Reliable Techniques for Solving Conformable Space-Time Fractional PHI-4 Model Arising in Nuclear Physics via β-derivative

Abstract

Nowadays, nonlinear fractional partial differential equations have been highly using for modelling of physical phenomena. Therefore, it is very important to achieve exact solutions of fractional differential equations for understanding complex phenomena in mathematical physics. In this study, new exact traveling wave solutions are reached of space-time fractional Phi-4 equation indicated by Atangana’s conformable derivative using two powerful different techniques. These are the functional variable method and the first integral method. Obtaining new solutions of this equation show that method is effective to understanding other nonlinear complex problems in particle and nuclear physics.

The Modified Exponential Function Method for Beta Time Fractional Biswas-Arshed Equation

“…where γ is any constant. When the derivative terms in Equation (10) are written instead of those obtained from the wave transformation (11), the general form of the following nonlinear ordinary differential equation is found:…”

“…Because such equations contain terms that represent many of the behaviors studied in these cases, each equation is defined as a mathematical model. To obtain the solutions of these mathematical models, there are various methods in the literature such as the improved Bernoulli subequation method [1], the trial equation method [2], the extended trial equation method [3], the G ′ /G method [4,5], the extended tanh method [6], the Kudryashov method [7,8], the generalized Kudryashov method [9], the new function method [10], the first integral method [11,12], the differential transform method [13], the variational iteration method [14], the exp-function method [15,16], the Adomian decomposition method [17], some numerical methods [18][19][20][21][22], the Chebyshev collocation method [23], the integral transform operator [24], the Chebyshev-Tau method [25], the Taylor expansion method [26], the modified exponential function method [27,28], and the new type F-expansion method [29].…”

A fractional-order mathematical model based on vaccinated and infected compartments of SARS-CoV-2 with a real case study during the last stages of the epidemiological event

“…It is known that integer order differential equations cannot always manage complex problems in nature. Nevertheless, the applications of fractional models can be seen in many fields such as physics, medicine, chemistry, and engineering [1] , [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] . Specifically, fractional modeling is a perfect tool for problems with complex mechanisms such as disease pandemics [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] .…”