Perera, Kanishka
Published in
Calculus of Variations and Partial Differential Equations

We prove an abstract critical point theorem based on a cohomological index theory that produces pairs of nontrivial critical points with nontrivial higher critical groups. This theorem yields pairs of nontrivial solutions that are neither local minimizers nor of mountain pass type for problems with combined nonlinearities. Applications are given to...

Bayrami-Aminlouee, Masoud Hesaaraki, Mahmoud Karim Hamdani, Mohamed Thanh Chung, Nguyen
Published in
Boundary Value Problems

In this paper, we study the effect of Hardy potential on the existence or nonexistence of solutions to the following fractional problem involving a singular nonlinearity: {(−Δ)su=λu|x|2s+μuγ+fin Ω,u>0in Ω,u=0in (RN∖Ω).\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbs...

Li, Changpin Li, Zhiqiang
Published in
Journal of Nonlinear Science

This paper is devoted to studying the blow-up and global existence of the solution to a semilinear time-space fractional diffusion equation, where the time derivative is in the Caputo–Hadamard sense and the spatial derivative is the fractional Laplacian. The mild solution of the considered semilinear equation by a convolution form is obtained, wher...

Guiñazú, Alex Vergara, Vicente
Published in
Journal of Pseudo-Differential Operators and Applications

In this paper we study large-time behavior evolution problems on the n-dimensional torus Tn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {T}^n$$\end{document}...

Alqahtani, Obaid
Published in
Advances in Difference Equations

In this paper, we obtain an approximate/analytical solution of nonlinear fractional diffusion equation using the q-homotopy analysis transform method. The existence and uniqueness of the solution for this problem are also derived. Further, the applicability of the model is discussed based on graphical results and numerical examples.

Jahanshahi, M. Golanbar, J. Ebadpour
Published in
International Journal of Applied and Computational Mathematics

In this paper, we consider some kind of fractional singular integral equations which they have weak and basic singularities in their kernels. In the first section, singularities are removed by changing of variables and change the order of integrals via Fubini’s theorem. In the second section, singularities are kind of basic. And we cannot remove or...

Youssfi, Ahmed Mahmoud, Ghoulam Ould Mohamed
Published in
Calculus of Variations and Partial Differential Equations

We consider a Lazer-Mckenna-type problem involving the fractional Laplacian and singular nonlinearity. We investigate existence, regularity and uniqueness of solutions in light of the interplay between the nonlinearities and the summability of the datum.

Khan, Hasib Ibrahim, Muhammad Abdel-Aty, Abdel-Haleem Khashan, M Motawi Khan, Farhat Ali Khan, Aziz
Published in
Chaos, solitons, and fractals

In this article, we are studying fractional-order COVID-19 model for the analytical and computational aspects. The model consists of five compartments including; ` ` S c ″ which denotes susceptible class, ` ` E c ″ represents exposed population, ` ` I c ″ is the class for infected people who have been developed with COVID-19 and can cause spread in...

Vázquez, Juan Luis
Published in
Calculus of Variations and Partial Differential Equations

We consider the natural time-dependent fractional p-Laplacian equation posed in the whole Euclidean space, with parameter 1

2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{documen...

Vougalter, Vitali Volpert, Vitaly
Published in
Analysis and Mathematical Physics

The article deals with the existence of solutions of an integro-differential equation in the case of anomalous diffusion with the negative Laplace operator in a fractional power in the presence of the transport term. The proof of existence of solutions is based on a fixed point technique. Solvability conditions for elliptic operators without the Fr...