In this paper, based on certain variable transformation, we apply the known (G’/G) method to seek exact solutions for three fractional partial differential equations: the space fractional (2+1)-dimensional breaking soliton equations, the space-time fractional Fokas equation, and the spacetime fractional Kaup-Kupershmidt equation. The fractional derivative is defined in the sense of modified Rie...

In this paper, the modified exponential function method is applied to find exact solutions of Radhakrishnan-Kundu-Lakshmanan equation with Atangana’s conformable beta-derivative. For this, definition beta derivative proposed by Atangana and properties are firstly given. Then, nonlinear which can be stated beta-derivative obtained using presented method. related problem in two solution cases obt...

The fractional derivatives in the sense of modified Riemann-Liouville derivative and the improved fractional sub-equation method are employed for constructing the exact solutions of nonlinear fractional partial differential equations. By means of this method, the space-time fractional generalized Hirota-Satsuma coupled Kortewegde Vries equations are successfully solved. As a result, three types...

We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for th...

This article applies the homotopy perturbation transform technique to analyze fractional-order nonlinear fifth-order Korteweg–de-Vries-type (KdV-type)/Kawahara-type equations. method combines Zain Ul Abadin Zafar-transform (ZZ-T) and (HPT) show validation efficiency of this investigate three examples. It is also shown that fractional integer-order solutions have closed contact with exact result...

This paper discuss the longstanding problems of fractional calculus such as too many definitions while lacking physical or geometrical meanings, and try to extend fractional calculus to any dimension. First, some different definitions of fractional derivatives, such as the Riemann-Liouville derivative, the Caputo derivative, Kolwankar’s local derivative and Jumarie’s modified Riemann-Liouville ...

We propose a new definition of a fractional-order Sumudu transform for fractional differentiable functions. In the development of the definition we use fractional analysis based on the modified Riemann-Liouville derivative that we name the fractional Sumudu transform. We also established a relationship between fractional Laplace and Sumudu duality with complex inversion formula for fractional S...

Thermoelastic modeling at nanoscale is becoming more important as devices shrink and heat sources are widely used in modern industries, such nanoelectromechanical systems. However, the conventional thermoelastic theories no longer applicable high-temperature settings. This study provides an insight into thermomechanical features of a nonlocal viscous half-space exposed to cyclic source. Using n...