Existence of solution for a nonlinear fractional elliptic system at resonance and nonresonance

Abstract

In this article, we study the existence of a weak solutions for the nonlinear fractional elliptic systems with Dirichlet boundary conditions in three cases. We use the Leray-Schauder degree and some sufficient conditions for the solvability of a resonance and non-resonance systems with respect to the spectrum of the fractional Laplacian.

Existence and uniqueness of distributional solution for semilinear fractional elliptic equation involving new operator and some numerical results

“…Recently, many methods have been proposed to deal with differential equation and fractional differential equations such as topological degree, 20,21 the upper and lower solutions method, 22 fixed‐point theory, 23–25 mountain pass method, 26 or the use of iteration methods 27,28 …”

“…Recently, many methods have been proposed to deal with differential equation and fractional differential equations such as topological degree, 20,21 the upper and lower solutions method, 22 fixed-point theory, [23][24][25] mountain pass method, 26 or the use of iteration methods. 27,28 In this article, we study the existence results for fractional partial differential equation involving new operator by using the Leray-Schauder degree theory.…”

Variable-order Implicit Fractional Differential Equations based on the Kuratowski MNC Technique

“…Fractional calculus is a branch of mathematical analysis that studies the possibility of taking real number powers or complex number powers of the differentiation and integration operators [9]. In the last thirty years, fractional calculus has contributed to a multitude of significant discoveries in pure and applied mathematics and various domains,such as chemistry [9], physics [16], biology [1], control theory [17], economics [12], biophysics [10], signal [24] and image processing, etc [8,7].…”

Existence and uniqueness of solution for a nonlinear fractional problem involving the distributional Riesz derivative

“…Fractional equations involving fractional derivatives have taken an important and valuable place among the different applied mathematical research subjects; this importance is due to its many applications in various scientific fields: mechanics, physics, image processing, electrochemistry, mathematical biology and viscoelasticity, and so on, for example, see previous works, 1–7 and the references therein, also to the variety of definitions of fractional derivative that are provided by researchers in this field such as Hilfer derivative, Caputo derivative, Marchaud derivative, Katugampola derivative, Atangana–Baleanu derivative, Davidson derivative, and Caputo Fabrizio derivative; see previous works 8–13 …”