In this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractio...

In this article, we define the fractional Mellin transform by using Riemann-Liouville fractional integral operator and Caputo fractional derivative of order [Formula: see text] and study some of their properties. Further, some properties are extended to fractional way for Mellin transform.

In this paper, a class of fractional advection-dispersion models (FADMs) is considered. These models include five fractional advection-dispersion models, i.e., the times FADM, the mobile/immobile time FADM with a time Caputo fractional derivative 0 < γ < 1, the space FADM with two sides Riemann-Liouville derivatives, the timespace FADM and the time fractional advection-diffusion-wave model with...

A new fractional subequation method is proposed for finding exact solutions for fractional partial differential equations (FPDEs). The fractional derivative is defined in the sense ofmodified Riemann-Liouville derivative. As applications, abundant exact solutions including solitary wave solutions as well as periodic wave solutions for the space-time fractional generalized Hirota-Satsuma coupled...

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...

An optimal control problem for the variable-order fractional-integer mathematical model of vaccination Covid 19 is presented in this research, where order derivatives varies during course time interval, becoming fractional or classical when it more favourable. The are defined here using both integral Riemann–Liouville and Caputo derivative. existence, uniqueness, boundedness positivity solution...

This paper delves into the extension and characterization of radial positive definite functions non-integer dimensions. We provide a thorough investigation by employing Riemann–Liouville fractional integral Caputo derivatives, enabling comprehensive understanding these functions. Additionally, we introduce secondary based on Bernstein completely monotone The practical significance our study is ...

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...

In this paper, the Caputo time varying singular fractional differential systems with delay and the Riemann-Liouville time varying singular fractional differential systems with delay are considered . By the D− inverse matrix and α − δ function, two fundamental solutions are given. The variation formulae for time varying singular fractional differential systems with delay are obtained. Mathematic...

In this paper, we first consider the general fractional derivatives of arbitrary order defined in Riemann–Liouville sense. particular, deduce an explicit form their null space and prove second fundamental theorem calculus that leads to a closed formula for projector operator. These results allow us formulate natural initial conditions differential equations with part develop operational Mikusi?...