Existence of 3-Weak Solutions for a New Class of an Overdetermined System of Fractional Partial Integro-Differential Equations

Abstract

The paper deals with the existence of three different weak solutions of [Formula: see text] -Laplacian fractional for an overdetermined nonlinear fractional partial Fredholm–Volterra integro-differential system by using variational methods combined with a critical point theorem due to Bonanno and Marano.

On Existence of Sequences of Weak Solutions of Fractional Systems with Lipschitz Nonlinearity

“…Lemma 8. Suppose that h i : ℝ ⟶ ℝ satisfy (3) and H i ðxÞ, Θ i ðxÞ, 1 ≤ i ≤ n defined through (20). Then, ΘðuÞ: X ⟶ ℝ be the functional that is described by…”

“…More and more efforts have been made in the fractional calculus field especially in FDEs (see, for instance, [2,5,[8][9][10][11][12][13][14][27][28][29][30][31][32][33][34][35][36][37][38][39]). Solution existence for a lot of boundary value problems and several nonlinear elementary problems is studied via a huge number of techniques and nonlinear mathematical tools (see [7,[15][16][17][18][19][20][21][22][23]): the theory of critical point, fixed-point theory, technique of monochromatic iterative, theory degree of coincidence, and the change methods. Motivated by multiple works involved in this domain, we concentrate in this paper on the existence of several infinite solutions to the following fractional-order differentiation system:…”

Numerical solution of the fractional‐order logistic equation via the first‐kind Dickson polynomials and spectral tau method

“…1 Recently, real-world models have been modeled through the fractional-order formulae due to their efficiency in constructing and ignoring the influence of outside forces as in physics, astronomy, chemistry, engineering, biology, mechanics, economics, and medicine. [2][3][4][5][6][7] There are huge modeled problems for many natural phenomena. 8 One of these significant models is the logistic problem.…”

Multiplicity Solutions of Fractional Impulsive p -Laplacian Systems: New Result

“…In viscoelasticity, electrochemistry, power, porous media, and electromagnetism, for instance, see and the references therein. Many articles have recently investigated the existence of solutions to boundary value problems for FDEs, and we refer the reader to one of them [2,[18][19][20][34][35][36][37][38][39][40][41][42][43][44][45][46] and the references therein. For example, Kamache et al [40] investigated the existence of three solutions for a class of fractional p-Laplacian systems using a variational structure and critical point theory.…”