On the development of Adomian decomposition method for solving PDE systems with non-prescribed data

Solvability of the boundary‐value problem for a mixed equation involving hyper‐Bessel fractional differential operator and bi‐ordinal Hilfer fractional derivative

“…where M 3 > 0, 𝜑 1k = − √ 𝜆 k 𝜑 k and we assume 𝜑 ′ ∈ L 2 (0, 1), provided that Δ k ≠ 0 for any k. From (34) and in the same way one can show that…”

“…32,33 We also refer that for solving partial differential equations (PDEs) powerful techniques have been using by several mathematicians so far. For example, in previous works 34,35 authors presented a new development of methodology based on Adomian decomposition method for solving PDEs and system of PDEs. Also, while in Kumar and Zeidan, 36 numerical solution of a non-linear fractional diffusion equation with advection and reaction terms is constructed, Lie group method is applied to investigate the symmetry group of transformations under which the governing time-fractional PDE remains invariant 37 (see also previous works 38,39 ).…”

Adapting a new formula to generalize multidimensional transforms

“…Partial differential equations are used to create the mathematical solution of physical and other problems involving functions of several variables, such as the propagation of heat or sound, fluid flow, elasticity, electrostatics, and electrodynamics. Solutions to partial differential equations can be achieved by some methods such as Laplace transforms, Homotopy method, the Chebyshev wavelet operational matrix method, the finite difference method, Adomian decomposition method, the residual power series method, and others [17][18][19][20][21][22][23][24][25].…”

Space time fractional Ito system with variable coefficients: explicit solution, conservation laws and numerical approximation

“…He started by doing a comprehensive symmetry classification of the nonlinear diffusion equation, considering thermal performance as a function of temperature. In Zeidan et al (2019Zeidan et al ( , 2022, Adomian decomposition method is used for solving partial differential equation (PDE) systems with nonprescribed data. In Kumar and Zeidan (2021), the efficient Mittag-Leffler kernel approach is utilize for time FDE, Exact solution (Bira et al, 2021;Mandal et al, 2018), numerical solutions (Kumar and Zeidan, 2022;Sultana et al, 2020), etc. In this article, the fractional power series method is used for solving the system of space time fractional partial differential equation with variable coefficient for explicit solution.…”

“…In Zeidan et al. (2019, 2022), Adomian decomposition method is used for solving partial differential equation (PDE) systems with nonprescribed data. In Kumar and Zeidan (2021), the efficient Mittag–Leffler kernel approach is utilize for time FDE, Exact solution (Bira et al.…”