Time-fractional generalized Boussinesq equation for Rossby solitary waves with dissipation effect in stratified fluid and conservation laws as well as exact solutions

Study of Ion‐Acoustic Solitary Waves in a Magnetized Plasma Using the Three‐Dimensional Time‐Space Fractional Schamel‐KdV Equation

“…Many of the physical processes that have been explored to date are nonconservative. It is important to be able to apply the power of fractional differentiation [8][9][10]. However, because of its nonlocal character, fractional calculus has not been used in physics and engineering.…”

Positive Solutions for a Fractional Boundary Value Problem with a Perturbation Term

“…Spurred by the extensively applicability of fractional derivatives in a variety of mathematical models in science and engineering [1][2][3], the subject of fractional differential equations with boundary value problems, which emerged as a new branch of differential equations, have attracted a great deal of attention for decades. As a small sampling of recent development, we refer the reader to [4][5][6][7][8][9][10][11][12][13][14].…”

Multiplicity for fractional differential equations with p-Laplacian

“…And there have been many results on existence and uniqueness of the solution of boundary value problems for fractional differential equations. For example, fractional boundary value problems at resonance [1,5,27,39,40], Caputo fractional derivative problems [11,23,37], impulsive problems [2,15,29,41], multi-point problems [1, 5, 21, 22, 27-29, 31, 40], integral boundary value problems [6,12,13,15], fractional p-Laplace problems [8,10,14,21,22,35,36], fractional lower and upper solution problems [4,7,30,38], fractional delay problems, [24,33,34], solitons [9], singular problems [3], etc.…”