Existence and uniqueness of solutions of Hahn difference equations

By Alaa E. Hamza, Samah M Ahmed. Advances in Differential Equations, 2013

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Hahn introduced the difference operator Dq,ωf(t)=(f(qt+ω)−f(t))/(t(q−1)+ω) in 1949, where 00 are fixed real numbers. This operator extends the classical difference operator Δωf(t)=(f(t+ω)−f(t))/ω as the Jackson q-difference operator Dqf(t)=(f(qt)−f(t))/(t(q−1)). In this paper, we present new results of the calculus based on the Hahn difference operator. Also, we establish an existence and uniqueness result of solutions of Hahn difference equations by using the method of successive approximations.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/0e969c16dca42c11eb0ae06a115316bc8d9bf2b6