Focus of this study is to cover up some gaps and further build up the theory of discrete fractional calculus. This dissertation starts with brief introduction and de nitions to discrete fractional calculus. Two new de ...

The aim of this study is to carry out detailed performance analysis of differential transformation method(DTM) for solving linear and non-linear differential equations. DTM is applied to obtain the analytical solution ...

The concept of centrality of a graph is introduced by Camille Jorden in 19th century for the analysis of different network models which is widely used in facility location problems. To measure the non-self-centrality ...

In this thesis, we meticulously construct an invariant Modi ed-Crank-Nicolson method that fast convergent to the exact solution of a one-dimensional non-linear heat equation. This innovative construction can be faithfully ...

Topological indices, sometimes also seen as graph-theoretic lters, maintain the order of molecular elements and provide mathematical language to predict features such as boiling points, radius of gyrations, viscosity, ...

Nearly all of the real world problems are non-linear in nature and they are coded in the language of non-linear differential equations. To find the exact solutions of these problems are usually impossible. So, we direct ...

This dissertation addresses the algebraic invariants such as depth, Stanley depth, projective dimension and regularity of some graphs. For this purpose, we investigate certain types of monomial ideals of polynomial rings ...