in this paper rationalized haar (rh) functions method is applied to approximate the numerical solution of the fractional volterra integro-differential equations (fvides). the fractional derivatives are described in caputo sense. the properties of rh functions are presented, and the operational matrix of the fractional integration together with the product operational matrix are used to reduce t...

Classical and anomalous diffusion equations employ integer derivatives, fractional derivatives, and other pseudodifferential operators in space. In this paper we show that replacing the integer time derivative by a fractional derivative subordinates the original stochastic solution to an inverse stable subordinator process whose probability distributions are Mittag-Leffler type. This leads to e...

The main aim of the paper is to present an algorithm solve approximately initial value problems for a scalar non-linear fractional differential equation with generalized proportional derivative on finite interval. condition connected one sided Lipschitz right hand side part given equation. An iterative scheme, based appropriately defined mild lower and upper solutions, provided. Two monotone se...

Abstract A newly proposed p -Laplacian nonperiodic boundary value problem is studied in this research paper the form of generalized Caputo fractional derivatives. The existence and uniqueness solutions are fully investigated for using some fixed point theorems such as Banach Schauder. This work supported with an example to apply all obtained new results validate their applicability.

In this work, radial basis function collocation method (RBFCM) is implemented for generalized time fractional Gardner equation (GTFGE). The RBFCM meshless and easy-to-implement in complex geometries higher dimensions, therefore, it highly demanding. the Caputo derivative of order ? (0, 1] used to approximate first whereas, Crank-Nicolson scheme hired space derivatives. numerical solutions are p...

The term fractional calculus is more than 300 years old. It is a generalization of the ordinary differentiation and integration to non-integer (arbitrary) order. The subject is as old as the calculus of differentiation and goes back to times when Leibniz, Gauss, and Newton invented this kind of calculation. In a letter to L’Hospital in 1695 Leibniz raised the following question (Miller and Ross...

The sub-title of this presentation could be “The fractional order integrator approach”. Although fractional order differentiation is commonly considered as the basis of fractional calculus, its effective basis is in fact fractional order integration, mainly because definitions, calculation and properties of fractional derivatives and Fractional Differential Systems (FDS) rely deeply on fraction...

‎This paper presents the numerical solution for a class of fractional differential equations. The fractional derivatives are described in the Caputo cite{1} sense. We developed a reproducing kernel method (RKM) to solve fractional differential equations in reproducing kernel Hilbert space. This method cannot be used directly to solve these equations, so an equivalent transformation is made by u...