in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

The Prabhakar fractional derivative model is not studied in the open literature for Casson fluid when vertical plate exhibits linear and quadratic translations with constant heating. Therefore, this study deals thermal transport of sodium alginate (C 6 H 9 NaO 7 ) over a temperature. Since classical PDEs are incapable analyzing investigating physical impact flow variables memory effects, develo...

the present study aims at indicating the existence and uniqueness result of system in extended colombeaualgebra. the caputo fractional derivative is used for solving the system of odes. in addition, rieszfractional derivative of colombeau generalized algebra is considered. the purpose of introducing rieszfractional derivative is regularizing it in colombeau sense. we also give a solution to a n...

approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. in this paper with central difference approximation and newton cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. three...

The space-fractional Poisson process is a time-changed homogeneous Poisson process where the time change is an independent stable subordinator. In this paper, a further generalization is discussed that preserves the Lévy property. We introduce a generalized process by suitably time-changing a superposition of weighted space-fractional Poisson processes. This generalized process can be related t...

In economics, depreciation functions (operator kernels) are certain decreasing functions, which assumed to be equal unity at zero. Usually, an exponential function is used as a function. However, in operator kernels do not allow simultaneous consideration of memory effects and effects. this paper, it proposed consider non-exponential type, simultaneously take into account by using the Prabhakar...

A universal approach by Laplace transform to the variational iteration method for fractional derivatives with the nonsingular kernel is presented; in particular, the Caputo-Fabrizio fractional derivative and the Atangana-Baleanu fractional derivative with the non-singular kernel is considered. The analysis elaborated for both non-singular kernel derivatives is shown the necessity of considering...