On a coupled system of fractional $ (p, q) $-differential equation with Lipschitzian matrix in generalized metric space

Abstract

<abstract><p>This work is concerned with the study of the existing solution for the fractional $ (p, q) $-difference equation under first order $ (p, q) $-difference boundary conditions in generalized metric space. To achieve the solution, we combine some contraction techniques in fixed point theory with the numerical techniques of the Lipschitz matrix and vector norms. To do this, we first associate a matrix to a desired boundary value problem. Then we present sufficient conditions for the convergence of this matrix to zero. Also, we design some algorithms to use the computer for calculate the eigenvalues of such matrices and different values of $ (p, q) $-Gamma function. Finally, by presenting two numerical examples, we examine the performance and correctness of the proposed method. Some tables and figures are provided to better understand the issues.</p></abstract>