Multiple Positive Solutions for a Class of Boundary Value Problem of Fractional$\left(p,q\right)$-Difference Equations under$\left(p,q\right)$-Integral Boundary Conditions

Abstract

This paper is mainly concerned with a class of fractional p , q -difference equations under p , q -integral boundary conditions. Multiple positive solutions are established by using the topological degree theory and Krein–Rutman theorem. Finally, two examples are worked out to illustrate the main results.

On Solvability of Fractional (p,q)-Difference Equations with (p,q)-Difference Anti-Periodic Boundary Conditions

“…p,q p ( α 2 ) Γ p,q (α) L s p α−1 d p,q s 0.00357786 < 1, that is, condition (12) is satisfied. Thus, all the conditions of Theorem 2 hold true and hence its conclusion implies that the problem in (15) and (16) Obviously, ϕ 1 = 1/20, ϕ 2 = 1/15, Ψ( ) = . In consequence 1 0.00284058, 2 0.00378745.…”

“…Clearly, all the conditions of Corollary 1 are satisfied. Therefore, the conclusion of Corollary 1 applies to the problem in (15) and (16). p,q p ( α 2 ) Γ p,q (α) L s p α−1 d p,q s 0.00357786 < 1, that is, condition (12) is satisfied.…”

“…In [14], some existence results for a boundary value problem of (p, q)-integrodifference equations with nonlocal fractional (p, q)-integral boundary conditions were presented. The existence of multiple positive solutions for a fractional (p, q)-difference equation under (p, q)-integral boundary conditions was discussed in [15]. More recently, the authors investigated the existence of solutions for a nonlinear fractional (p, q)-difference equation subject to separated nonlocal boundary conditions in [16], whereas some existence results for a sequential fractional Caputo (p, q)-integrodifference equation with three-point fractional Riemann-Liouville (p, q)-difference boundary conditions were obtained in [17].…”

Approach and Landing Aircraft Wake Encounter Risk Based on Reynolds-Averaged Navier-Stokes Numerical Simulation

“…The fuselage can be considered a slender cylinder with a small angle of attack. According to the slender spin International Journal of Aerospace Engineering linearization theory, its lift change can be expressed by [20]…”