... method Caputo fractional derivative Parameter estimation Critical parameter Fractional calculus has emerged as a powerful mathematical tool for modelling systems with memory and hereditary properties (Podlubny, 1998 ; Kilbas et al., 2006 ; Gorenflo and Mainardi, 1997 ; Xue, 2017...

... Publishing Limited Licensed re-use rights only Caputo fractional derivative Heat transfer problems Nonlinear differential equations Numerical methods Symbol Description T a = Ambient temperature; θ ( t ) = Dimensionless temperature; λ...

..., namely gold, copper, silver, zinc oxide, magnesium oxide, titanium oxide and alumina, while the Caputo fractional derivative is used to account for the memory and hereditary characteristics of blood flow that are neglected in conventional integer-order models. The transformed governing equations...

... ∂ t α to maintain the dimensional consistency, where C ˜ d i f f ( T α − 1 ) is known as a diffusive coefficient. The boundary conditions are presented in Figure 1(a)–(c) . Caputo fractional derivative Porous media Entropy generation Cu-water...

...) The Laplace transform of Caputo fractional derivative for m – 1 < α ≤ m, m ∈ ℕ, can be determined in the form of: L [ D α f ( x ) ] = s m F ( s ) − s m − 1 f ( 0 ) − s m − 2 f ′ ( 0 ) − … − f ( m − 1 ) ( 0 ) s m − α...

...) by using cubic B-spline method. Assistant Professor Talaat El-Sayed El-Danaf can be contacted at: talaat11@yahoo.com © Emerald Group Publishing Limited 2014 Adomian decomposition method Caputo fractional derivative Variation iteration method (Equation 1) Fractional order...

... differential equation Homotopy analysis method Variational iteration method Caputo fractional derivative Series solution Differential equations Mathematics The homotopy analysis method (HAM) is developed by Liao (1992) . Based on homotopy of topology, the validity of the HAM is independent...

... Ahmet Yıldırım can be contacted at: ahmetyildirim80@gmail.com © Emerald Group Publishing Limited 2012 Population dynamics Caputo fractional derivative Differential transform method Padé approximants Fractional integro‐differential equation Mathematical analysis Modelling...

... no method that yields an exact solution for a fractional differential equation. Only approximate solutions can be derived using the linearization or perturbation methods. Flow Differential equations Foams Homotopy perturbation method Variational iteration method Caputo fractional derivative...