The formulations of Riemann-Liouville and Caputo derivatives in the complex plane are presented. Two versions corresponding to the whole or half plane. It is shown that they can be obtained from the Grünwald-Letnikov derivative.

In this research article, the constant proportional Caputo approach of fractional derivative is applied to derive generalized thermal and molecular profiles for flow second grade fluid over a vertical plate. The governing equations prescribed model are reduced dimensionless form then solved temperature, concentration, velocity via Laplace transform. Further graphs field variables sketched param...

In this paper an algorithm for approximate solving of a boundary value problem nonlinear differential equation with special type fractional derivative is suggested. This called generalized proportional Caputo derivative. The new based on the application monotone-iterative technique combined method lower and upper solutions. connection this, initially, linear condition studied, its explicit solu...

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

In this article, by using the technique of upper and lower solutions, some comparison results for first-order fuzzy differential equations are established. Hukuhara derivative, difference, partial orderings used proving theorems. We extend our to initial time difference case as well. Also, practicality these is demonstrated giving an example.

We study hybrid fuzzy differential equations (HFDEs) under the Hukuhara derivative numerically using Picard’s and general linear method (GLM). use trapezoidal triangular numbers as initial conditions. To demonstrate efficiency of proposed methods, exact well numerical solutions are presented graphically. In addition, a comparison is made between results from applying GLM those obtained when fif...

Variational iteration method is introduced to solve two-point boundary value problem for a second order fuzzy differential equation under generalized Hukuhara differentiability. To illustrate the ability and reliability of the method, some examples are given, revealing its effectiveness and simplicity.

In this paper, the fractional Sturm-Liouville problems, in which the second order derivative is replaced by a fractional derivative, are derived by the Homotopy perturbation method. The fractional derivatives are described in the Caputo sense. The present results can be implemented on the numerical solutions of the fractional diffusion-wave equations. Numerical results show that HPM is effectiv...

In this paper, we present a convergent collocation method with which to find the numerical solution of generalized fractional integro-differential equation (GFIDE). The presented approach is based on using Jacobi poly-fractonomials. GFIDE defined in terms B-operator introduced recently, and it reduces Caputo derivative other derivatives special cases. convergence error analysis proposed are als...