In this study, we introduced a novel scheme to attain approximate and closed-form solutions of conformable Newell-Whitehead-Segel (NWS) equations, which belong the most consequential amplitude equations in physics. The Shehu transform (CST) Adomian decomposition method (ADM) are combined proposed method. We call it (CSDM). To assess efficiency consistency recommended method, demonstrate 2D 3D g...

In this paper, we investigate inverse source problems for a wide range of PDEs parabolic and hyperbolic types as well time-fractional evolution equations by partial interior observation. Restricting the terms to form separated variables, establish uniqueness results simultaneously determining both temporal spatial components without non-vanishing assumptions at [Formula: see text], which seems ...

Image inpainting is the process of repairing damaged or missing areas an image by utilizing information from its surrounding environment. The fractional order operator, which processes details like textures and edges with a finer scale, has demonstrated better outcomes success in processing. This study draws inspiration definition singular integral Laplacian presents two adaptive variational fu...

In this article, the (G ′ /G)-expansion method has been implemented to find the travelling wave solutions of nonlinear evolution equations of fractional order. For this, the fractional complex transformation method has been used to convert fractional order partial differential equation to ordinary differential equation. Then, (G ′ /G)-expansion method has been implemented to celebrate the serie...

Group-theoretic methods based on local symmetries are useful to construct invariant solutions of PDEs and to linearize nonlinear PDEs by invertible mappings. Local symmetries include point symmetries, contact symmetries and, more generally, Lie-Biicklund symmetries. An obvious limitation in their utility for particular PDEs is the non-existence of local symmetries. A given system of PDEs with a...

This paper systematically explains how to apply the invariant subspace method using variable transformation for finding exact solutions of (k+1)-dimensional nonlinear time-fractional PDEs in detail. More precisely, we have shown transform given into (1+1)-dimensional procedure. Also, explain derive reduced equations method. Additionally, this careful and systematic study, will investigate find ...

P artial differential equations (PDEs) arise in numerous scientific and engineering applications. Mathematical modeling in various applications often ends up with a set of PDEs. Mathematical techniques can help to understand many crucial properties of the PDEs, such as existence and uniqueness of solutions under suitable initial and/or boundary conditions, and the well-posedness of the problem,...

This study investigates the wave solutions of time-fractional Sawada–Kotera–Ito equation (SKIE) that arise in shallow water and many other fluid mediums by utilizing some most flexible high-precision methods. The SKIE is a nonlinear integrable partial differential (PDE) with significant applications dynamics mechanics. However, traditional numerical methods used for analyzing this are often pla...

This study is motivated by the recent development in the fractional calculus and its applications. During last few years, several different techniques are proposed to localize the nonlocal fractional diffusion operator. They are based on transformation of the original problem to a local elliptic or pseudoparabolic problem, or to an integral representation of the solution, thus increasing the di...

By introducing the fractional derivatives in the sense of caputo, we use the Adomian decomposition method to construct the approximate solutions for some fractional partial differential equations with time and space fractional derivatives via the time and space fractional derivatives wave equation, the time and space fractional derivatives reduced wave equation and the (1+1)-dimensional Burger’...