Abstract
We consider some classes of space- and time-fractional telegraph equations in complex domain in sense of the Riemann-Liouville fractional operators for time and the Srivastava-Owa fractional operators for space. The existence and uniqueness of holomorphic solution are established. We illustrate our theoretical result by examples.
Highlights
Fractional differential equations have emerged as a new branch of applied mathematics which has been used for many mathematical models in science and engineering
Various types play important roles and tools in mathematics and in physics, control systems, dynamical systems, and engineering to create the mathematical modeling of many physical phenomena
The telegraph equation appears when we look for a mathematical model for the electrical flow in a metallic cable
Summary
Fractional differential equations have emerged as a new branch of applied mathematics which has been used for many mathematical models in science and engineering. Various types play important roles and tools in mathematics and in physics, control systems, dynamical systems, and engineering to create the mathematical modeling of many physical phenomena Journal of Function Spaces and Applications signals and used in modeling reaction diffusion 11, Numerical solutions for these equations are posed; for example, the Adomian decomposition method ADM and homotopy perturbation method HPM were used to solve the space- and time-fractional telegraph equations see , Variational iteration method VIM was used to solve the linear and nonlinear telegraph equation see 14–16. The fractional derivative for the space is taken in the sense of the Srivastava-Owa operators while the fractional time derivative is taken in the sense of the Riemann-Liouville operators because the Riemann-Liouville fractional derivative could hardly pose the physical interpretation of the initial conditions required for the initial value problems involving fractional differential equations. One says that a x A x if and only if |ai| ≤ |Ai| for each i
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