Fractional p-Laplacian Equations with Sandwich Pairs

Abstract

The main purpose of this paper was to consider new sandwich pairs and investigate the existence of a solution for a new class of fractional differential equations with p-Laplacian via variational methods in ψ-fractional space Hpα,β;ψ(Ω). The results obtained in this paper are the first to make use of the theory of ψ-Hilfer fractional operators with p-Laplacian.

Numerical Algorithms for Approximation of Fractional Integrals and Derivatives Based on Quintic Spline Interpolation

“…In order to calculate, for example, the time or space fractional integrals and/or derivatives at a given time or a given point, then knowledge of the function at all previous times or positions is required. There are many applications of fractional calculus in the fields of science and engineering (see, e.g., recent works [5][6][7][8][9][10][11]), and it is impossible to list all their applications.…”