... < α < 1 where f : R → R , t → f ( t ) denotes a continuous function. D efinition 2. The Caputo fractional derivative [ 1 , 2 ] of order α is defined as follows: (1.4) D t α f ( t ) = { 1 Γ ( 1 − α ) ∫ 0 t f ′ ( ξ...

... method generalized Hirota–Satsuma equation Caputo fractional derivative The role of mathematics in order to describe all the phenomena arise in daily life is essential and stimulating. Humankind designed the novel and important weapon within the frame of mathematics in order to deal with all...

... ( t ) , y ( t ) ) = 0 subject to the initial conditions (12) x ( 0 ) = x 0 ,     y ( 0 ) = y 0 where D α i is the Caputo fractional derivative of order 0 < α i ≤ 1 and g i is a nonlinear function...

... matrix inequalities. Finally, a numerical example and fractional order Van der Pol system are given to show the effectiveness of our results. Caputo fractional derivative fractional order uncertain T-S fuzzy model stability PDC state feedback control Fractional calculus as an extension...

... the correlation coefficients, are avoided. Caputo fractional derivative fractional Klein–Gordon Haar wavelet method Klein–Gordon equations function-approximation operational matrix numerical solution In the last few decades, fractional calculus found many applications in various fields...