An elastic beam equation (EBEq) described by a fourth-order fractional difference equation is proposed in this work with three-point boundary conditions involving the Riemann–Liouville fractional difference operator. New sufficient conditions ensuring the solutions’ existence and uniqueness of the proposed problem are established. The findings are obtained by employing properties of discrete fractional equations, Banach contraction, and Brouwer fixed-point theorems. Further, we discuss our problem’s results concerning $\mathcal{H}$yers–$\mathcal{U}$lam ($\mathcal{HU}$), generalized $\mathcal{H}$yers–$\mathcal{U}$lam ($\mathcal{GHU}$), $\mathcal{H}$yers–$\mathcal{U}$lam–$\mathcal{R}$assias ($\mathcal{HUR}$), and generalized $\mathcal{H}$yers–$\mathcal{U}$lam–$\mathcal{R}$assias ($\mathcal{GHUR}$) stability. Specific examples with graphs and numerical experiment are presented to demonstrate the effectiveness of our results.

The results reported in this paper are concerned with the existence and uniqueness of solutions of discrete fractional order two-point boundary value problem. The results are developed by employing the properties of Caputo and Riemann–Liouville fractional difference operators, the contraction mapping principle and the Brouwer fixed point theorem. Furthermore, the conditions for Hyers–Ulam stability and Hyers–Ulam–Rassias stability of the proposed discrete fractional boundary value problem are established. The applicability of the theoretical findings has been demonstrated with relevant practical examples. The analysis of the considered mathematical models is illustrated by figures and presented in tabular forms. The results are compared and the occurrence of overlapping/non-overlapping has been discussed.

The Lotka – Volterra systems served as a basis for the development and analysis of more realistic mathematical models of nonlinear interactions. A new form of discrete time 2-D prey predator model involving Lesile - Gower functional response with step size is proposed for discussion. Utilizing Euler scheme, discrete system is obtained from the continuous dynamical system. Dynamical consistency of the model which includes the existence and stability of the fixed points is investigated. Eigenvalues of Jacobian matrix are computed for corresponding fixed points. Analytical results illustrate rich dynamics and complexity of the model. The bifurcation theory is employed to study the existence of flip and Neimark-Sacker bifurcations. The chaos control of the discrete system is performed and numerical simulations are provided supporting the results.

This paper examines the dynamical nature of a prey - predator – scavenger involving harvesting on predator population. A discretization process is applied to the fractional order system and its discrete version is obtained. Existence of possible fixed points is established and the local stability analysis is carried out. It is also proved that the system under goes Neimark-Sacker (NS) and Period-Doubling bifurcation (PDB) at certain parametric values for interior fixed point with the help of an explicit criterion for NS and PDB. Numerical simulations are performed for the model with quadratic harvesting on predator. Also the existence of limit cycles is shown and bifurcation diagrams are plotted for selected range of growth parameter.