Multiplicity of Solutions for Fractional-Order Differential Equations via the κ(x)-Laplacian Operator and the Genus Theory

Abstract

In this paper, we investigate the existence and multiplicity of solutions for a class of quasi-linear problems involving fractional differential equations in the χ-fractional space Hκ(x)γ,β;χ(Δ). Using the Genus Theory, the Concentration-Compactness Principle, and the Mountain Pass Theorem, we show that under certain suitable assumptions the considered problem has at least k pairs of non-trivial solutions.

Existence, Uniqueness and the Multi-Stability Results for a W-Hilfer Fractional Differential Equation

“…Jung, Rezaei and Rassias [9] studied the Ulam stability of ODEs by the Laplace transform technique. Applying the UHR technique, Baleanu and Wu [10] demonstrated the Mittag-Leffler (ML)-type stability of fractional equations; Baleanu, Wu and Huang [11] demonstrated the ML-type stability of fractional delay difference equations with impulse; Wu [12] proved the ML-type stability of fractional neural networks through the fixed point (FP) theory see also [13].…”