TY - JOUR
TI - A new approach to fractional differential equations
AU - Alrabaiah Hussam
AU - Hussain Sultan
AU - Awan Sami Abdul
AU - Zeb Anwar
AU - Shah Kamal
AU - Abdeljawad Thabet
JN - Thermal Science
PY - 2023
VL - 27
IS - 101
SP - 301
EP - 309
PT - Article
AB - In this work, we define fractional derivative of order ς > 0, with no  restrictions on the domain of the function, and give its geometry. We derive  some rules and properties for the proposed new approach and show that if  fractional order converges to an integer order, then each rule converges to  the corresponding rule of derivative under this integer. On applications  side we show that it has ability to convert various type of FDE to ODE and  vice versa. Finally, we solve several FDE given in literature through the  new approach.