A novel hybrid technique to obtain the solution of generalized fractional-order differential equations

A Fixed Point Theorem for Time-Fractional Fornberg-Whitham Equation Arising in Atmospheric Science

“…Its non-linearity trait makes it very difficult to find an exact solution, and the discrete point findings of numerical approaches do not provide consistency. To address this problem, a number of researchers have provided techniques, such as the sine Gordon expansion method [16][17][18][19], the Homotopy analysis method [20][21], the Bernoulli sub-equation function method [22], the generalized exponential rational function method [23], the He's variational iteration method [24][25][26], the Homotopy perturbation technique [27][28][29], the Chebyshev spectral collocation method [30], the rational sine-cosine and rational sinh-cosh methods [31], the conformable derivative [32], the timefractional Caputo derivative [33], the Atangana-Baleanu derivatives [34], the fractional residual power series method [35], the Residual Power Series Method [36], semi-analytic technique to deal with nonlinear fractional differential equations [37]. For more details we can refer to [38].…”

Ulam–Hyers Stability of Linear Differential Equation with General Transform

“…The general integral transform was initially proposed by Jafari [19] in 2021, which is later called the Jafari transform, and Jafari-Yang transform [20][21][22]. In [23], the authors employed both the Haar wavelets collocation method and the Homotopy perturbation general transform technique. In [24], the authors proposed the Atangana-Baleanu-Caputo fractional derivative operator in the generalized integral transform sense.…”

On the semi-analytic technique to deal with nonlinear fractional differential equations

“…In recent years, many hybrid methods have been introduced that combine the integral transforms with semi-analytic techniques such as the Sumudu Adomian decomposition method [16], Laplace variational iteration method [17], residual power series method (RPSM) [18,19], homotopy perturbation general transform method [20] and homotopy analysis Sumudu transform method [21] to solve the fractional differential equation (FDE). In continuation of the study, the authors here in the present work introduce another powerful method as a combination of the homotopy perturbation method (HPM) [22,23] and the Sawi transform [3], and call it: the homotopy perturbation Sawi transform method (HPSTM), which is capable of dealing with general FDE in an efficient manner, and can be applied not only on various nonlinear wave equations, oscillatory equations with discontinuities and boundary value problems, but it can also deal with different kinds of nonlinear equations.…”