We correct a recent result concerning the fractional derivative at extreme points. We then establish new results for the Caputo and Riemann-Liouville fractional derivatives at extreme points.

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 given article describes the implicit fractional dierential equation with anti-periodic boundary conditionsin frame of Caputo-Katugampola derivative. We obtain an analogous integral thegiven problem and prove existence uniqueness results such a using Banach andKrasnoselskii xed point theorems. Further, by applying generalized Gronwall inequality, Ulam-Hyersstability are discussed. To show ee...

In this paper, we prove the existence and uniqueness of solution to the impulsive fuzzy functional differential equations under generalized Hukuhara differentiability via the principle of contraction mappings. Some examples are provided to illustrate the result.

Abstract In this work, we study the existence, uniqueness, and continuous dependence of solutions for a class fractional differential equations by using generalized Riesz operator. One can view results work as refinement existence theory with Riemann–Liouville, Caputo, classical derivative. Some special cases be derived to obtain corresponding equations. We provide an illustrated example unique...

In this paper, by differentiating the entropy’s generating function (i.e., h(t) = R SX̄F tX (x)dx) using a Caputo fractional-order derivative, we derive generalized non-logarithmic fractional cumulative residual entropy (FCRE). When order of differentiation α → 1, ordinary Rao CRE is recovered, which corresponds to results from first-order differentiation. Some properties and examples proposed F...

In this paper, we present a numerical computational approach for solving Caputo type fractional differential equations. This method is based on approximation of Caputo derivative in terms of integer order derivatives and waveform relaxation method. The utility of the method is shown by applying it to several examples. A comparative study indicates that our approach is more efficient and accurat...

In this paper, we investigate numerical approximations of the scalar conservation law with the Caputo derivative, which introduces the memory effect. We construct the first order and the second order explicit upwind schemes for such equations, which are shown to be conditionally 1 contracting and TVD. However, the Caputo derivative leads to the modified CFL-type stability condition, ( t) = O( x...

in this paper we introduce a type of fractional-order polynomials basedon the classical chebyshev polynomials of the second kind (fcss). also we construct the operationalmatrix of fractional derivative of order $ gamma $ in the caputo for fcss and show that this matrix with the tau method are utilized to reduce the solution of some fractional-order differential equations.