Abstract:
In this dissertation, we discussed existence, uniqueness and stability of di erent types of fractional
di erence equations in delta and nabla sense.
Existence and stability results for a class of non-linear Caputo nabla fractional di erence
equations are obtained using xed point theorems including Schauder's xed point theorem,
the Banach contraction principle and Krasnoselskii's xed point theorem. Furthermore, results
depends on the structure of nabla discrete Mittag-Le er functions. Existence and uniqueness
of solution for impulsive fractional di erence equation is investigated through xed point theorems
including the Banach contraction principle, Schaefer's xed point theorem and nonlinear
alternative Leray Schauder theorem. Moreover, Ulam's type stability of problem in delta sense
is discussed using newly developed Gronwall inequality. Using existing q-fractional Gronwall
inequality, Ulam-Hyers stability and the Ulam-Hyers-Rassias stability is discussed for a delay
Caputo q-fractional di erence system.
Using newly developed Gronwall-Bellman inequality, we discussed Ulam-Hyers stability of
Caputo nabla fractional di erence system. Existence of solution of p-Laplacian fractional difference
equations in nabla sense is discussed using Schaefer's xed point theorem and then
Ulam-Hyers stability is examined. Furthermore, we discussed Ulam-Hyers-Mittag-Le er and
Ulam-Hyers-Rassias-Mittag-Le er stability for a class of Caputo nabla fractional order delay
di erence equation using Banach xed point theorem in generalized complete metric space and
using Chebyshev norm. Moreover, we obtained existence and stability results for a fractional
di erence Langevin equation within nabla Caputo fractional di erence and subject to non-local
boundary conditions using xed point theorems.
