I am working on designing of microstrip lines and its behavior with ebg structures. i am unable to find the design equations for microstip line length and width for a particular resonance frequency.
generally, the width of a microstrip line, its height above the ground plane, and the permittivity (and permeability) of the intervening material determine the impedance of the line. Please have a look at the book:
Gupta, Garg, Bahl, Bhartia: "Microstrip Lines and Slotlines", 2nd ed., 1996, Artech House, Inc.
You can also check your results using one of the online calculators, e. g.:
https://www.eeweb.com/tools/microstrip-impedance
The speed of propagation depends on the permittivity and permeability of the base material, too (speed = 1 / sqrt(permittivity * permeability)). From this speed follows the wavelength at a certain frequency (wavelength = speed / frequency). Microstrip lines (as well as other lines) are resonant if their length equals 1/2 wavelength or an integer multitude thereof.
However, I'm not sure whether your application demands resonant lines, or if the lines are just used to stimulate the resonant material. In the second case, the impedance of the line should equal the impedance of the signal source (resp. the impedance of the connecting cable), and the line should be terminated by a resistor having the same impedance. The only effect of the length of the properly terminated line is the attenuation of the signal which depends mainly on the loss in the base material.