A Langevin-Type q-Variant System of Nonlinear Fractional Integro-Difference Equations with Nonlocal Boundary Conditions

We introduce a new class of boundary value problems consisting of a q-variant system of Langevin-type nonlinear coupled fractional integro-difference equations and nonlocal multipoint boundary conditions. We make use of standard fixed-point theorems to derive the existence and uniqueness results for the given problem. Illustrative examples for the obtained results are also presented.

On exact solutions of fractional differential-difference equations with Ψ-Riemann–Liouville derivative

The aim of this work is to modify the invariant subspace method (ISM) in order to obtain closed form solutions of fractional differential-difference equations with Ψ-Riemann–Liouville (Ψ-RL) fractional derivative for first time. We have investigated the cases of two-dimensional and the three-dimensional invariant subspaces (ISs) in the suggested scheme. Using the modified ISM, new exact generalized solutions for the general fractional mKdV Lattice equation and the fractional Volterra lattice system are obtained. Compared with similar solution techniques in literature, the presented solution scheme is highly efficient and is capable to find new general exact solutions which cannot be attained by other methods.

Symmetries and Solvability of a Class of Higher Order Systems of Ordinary Difference Equations

We perform Lie analysis for a system of higher order difference equations with variable coefficients and derive non-trivial symmetries. We use these symmetries to find exact formulas for the solutions in terms of k. Furthermore, a detailed study for a specific value of k is presented. Our findings generalize some results in the literature.