Adomian decomposition method has been employed to obtain solutions of a system of nonlinear fractional differential equations: D i yi (x)=Ni(x, y1, . . . , yn), y i (0)= c k, 0 k [ i ], 1 i n and D i denotes Caputo fractional derivative. Some examples are solved as illustrations, using symbolic computation. © 2005 Elsevier B.V. All rights reserved.

In this present study, we investigate the solutions for fractional kinetic equations involving k-Struve function using the Sumudu transform. The graphical interpretations of the solutions involving k-Struve function and its comparison with generalized Bessel function are given. The methodology and results can be considered and applied to various related fractional problems in mathematical physics.

In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.

In this note we consider colorings of series-parallel graphs. Specifically, we provide bounds on their fractional and circular chromatic numbers and the defective version of these parameters. The main result is that the fractional chromatic number of any series-parallel graph of odd girth k is exactly 2k/(k − 1).

The authors discover a general k-fractional integral identity with multi-parameters for twice differentiable functions. By using this integral equation, the authors derive some new bounds on Hermite–Hadamard’s and Simpson’s inequalities for generalized (m,h)-preinvex functions through k-fractional integrals. By taking the special parameter values for various suitable choices of function h, some...

The concepts of (k; d)-coloring and the star chromatic number, studied by Vince, by Bondy and Hell, and by Zhu are shown to reeect the cographic instance of a wider concept, that of fractional nowhere-zero ows in regular matroids.

In this paper, first, a new predictor-corrector method( called the modified predictorcorrector method ) for the fractional differential equations is developed. And the new method can be formally viewed as a modification as the classical predictor-corrector method. Second, it is proved that the numerical accuracy of this new method is superior to that of the classical predictorcorrector method b...

This paper is concerned with the existence of solutions for a new boundary value problem nonlinear coupled (k,?)–Hilfer fractional differential equations subject to (k,?)–Riemann–Liouville integral conditions. We prove two results by applying Leray–Schauder alternative, and Krasnosel’ski?’s fixed-point theorem under different criteria, while third result, concerning uniqueness given problem, re...

We conjecture that any graphG with treewidth k and maximum degree ∆(G) ≥ k + √ k satisfies χ′(G) = ∆(G). In support of the conjecture we prove its fractional version.