On the weak solutions of an overdetermined system of nonlinear fractional partial integro-differential equations

Abstract

In this research work, we employ the critical point theory based on the variational structure to prove the existence of at least three distinct weak solutions for an overdetermined system of nonlinear fractional partial Fredholm-Volterra integro-differential equations.

Some New Results for the Sobolev-Type Fractional Order Delay Systems with Noncompact Semigroup

“…Many mathematicians have devoted themselves to the study of fractional differential equations for a long time and have made important contributions to theory and application of fractional differential equations. For more details about fractional calculus and fractional differential equations, we refer to the monographs [1][2][3] and the papers [4][5][6][7][8][9]. At present, much interest has been developing in the fractional differential inclusions, and we refer readers to [10,11] and the references therein.…”

Multiplicity of Weak Positive Solutions for Fractional p & q Laplacian Problem with Singular Nonlinearity

“…In recent years, the fractional Laplacian problems have been extensively investigated. For more details, we cite the reader to [11][12][13][14][15]. ere are many different definitions of weak solutions for the fractional Laplacian equation (3).…”

Existence of ground state for fractional Kirchhoff equation with $L^{2}$ critical exponents

“…Equation 2comes from free vibrations of elastic strings by taking into account the changes in length of the string produced by transverse vibrations [13]. After the pioneering works [17] and [15], equation (1) has attracted considerable attention. The existence and asymptotic behavior of nodal solutions of equation (1) were considered by Deng, Peng, and Shuai [5].…”

“…Hence some mathematicians considered equation (1) by studying some constrained variational problems and obtained the existence of ground state of equation (1). This technique was generally used for other types of equations, for example, semilinear Schrödinger equation [11,24], Schrödinger-Poisson equation [4,12], quasilinear Schrödinger equation [29,30]; see also [1,2,18,21,22]. For s = 1, as far as we know, the first work comes from Ye [25], who considered the following minimization problem:…”