Regularization of a multidimensional diffusion equation with conformable time derivative and discrete data

Abstract

In this paper, we consider a backward problem for a nonlinear diffusion equation with a conformable derivative in the case of multidimensional and discrete data. We show that this problem is ill‐posed and then we establish stable approximate solutions by two different regularization methods: the Fourier truncated method and the quasi‐boundary value (QBV) method. Furthermore, the error between the approximate solution and the sought solution is given.

Monotone Iterative Technique for Nonlinear Periodic Time Fractional Parabolic Problems

“…Binh et al [12] have considered the initial inverse problem for a diusion equation with a conformable derivative in a general bounded domain. Tuan et al [44] have studied a backward problem for a nonlinear diusion equation with a conformable derivative in the case of multidimensional and discrete data. Tuan et al [45] have considered an inverse problem of recovering the initial value for a generalization of timefractional diusion equation, where the time derivative is replaced by a regularized hyper-Bessel operator.…”

Controllability of Mild Solution of Nonlocal Conformable Fractional Differential Equations

“…This novel fractional derivative is very simple and verifies all the properties of the classical deriva-tive. Actually, the conformable fractional derivative becomes the subject of many research contributions [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39].…”

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

“…The ERFM has been widely used to obtain a series of exact solutions for higher‐dimensional nonlinear PDEs and fractional PDEs 14–24 . Recently, Wang et al 25 introduced a monotone iterative method for solving a nonlinear fractional conformable p‐Laplacian differential system, Hayman Thabet and Subhash Kendre 10 provided a conformable differential transform for solving nonlinear conformable partial differential equations, Cenesiz et al 26 studied PDEs with conformable derivative using the first integral method, Thabet et al 27 obtained analytical solutions for wave equations of conformable derivatives by using generalized conformable differential transform, Hosseini et al 7 applied the Kudryashov method for Klein‐Gordon equations with conformable derivatives, H. C. Erdik Yaslan 28 used the tanh method with the fractional complex transform to solve the conformable Kawahara equation, Khodadad et al 29 introduced the sub‐equation method to obtain a solution for Zakharov‐Kuznetsov equation with conformable derivatives, and Tuan et al 30 established stable approximate solutions for a nonlinear diffusion equation with a conformable derivative in the case of multidimensional and discrete data by using two different regularization methods: the Fourier truncate method and the quasi‐boundary value method.…”