Abstract
In this paper, we study nonlinear fractional (p,q)-difference equations equipped with separated nonlocal boundary conditions. The existence of solutions for the given problem is proven by applying Krasnoselskii’s fixed-point theorem and the Leray–Schauder alternative. In contrast, the uniqueness of the solutions is established by employing Banach’s contraction mapping principle. Examples illustrating the main results are also presented.
Highlights
Fractional differential equations have been considered a popular field of research and have attracted many researchers’ attention
In the last two decades, the fractional differential equations have developed from theoretical aspects of the existence and uniqueness of solutions to analytic and numerical methods for finding solutions, which can be found in [1,2,3,4,5,6,7,8,9]
In modern mathematical analysis, fractional differential equations have a range of applications, such as engineering and clinical disciplines, including biology, physics, chemistry, economics, signal and image processing, and control theory; see [10,11,12,13,14,15,16,17] for more details
Summary
Fractional differential equations have been considered a popular field of research and have attracted many researchers’ attention. We study the existence and uniqueness of solutions of the nonlocal boundary value problem of nonlinear fractional ( p, q)-difference equations given by c D α y ( t ) = h ( t, y ( pα t )), t ∈ [0, T/pα ], 1 < α ≤ 2, p,q (4). Β 1 y(0) + γ1 D p,q y(0) = ζ 1 y(η1 ), β 2 y( T ) + γ2 D p,q y( T/p) = ζ 2 y(η2 ), where h ∈ C([0, T/pα ] × R, R) and β i , γi , ηi (i = 1, 2) are constants; c D αp,q and D p,q are the fractional ( p, q)-derivative of the Caputo type and the first-order ( p, q)-difference operator, respectively
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