Abstract
In this paper we introduced the conformable derivatives and integrals of radial basis functions (RBF) to solve conformable fractional differential equations via RBF collocation method. For that, firstly, we found the conformable derivatives and integrals of power, Gaussian and multiquadric basis functions utilizing the rule of conformable fractional calculus. Then by using these derivatives and integrals we provide a numerical scheme to solve conformable fractional differential equations. Finally we presents some numerical results to confirmed our method
Highlights
In conjunction with the development of theoretical progress of fractional calculus, a number of mathematicians have started to applied the obtained results to real world problems consist of fractional derivatives and integrals [1, 2]
An significant point is that the fractional derivative at a point x is a local property only when a is an integer; in non-integer cases we cannot say to order a is often defined by means of the Fourier or Mellin integral transforms
In this paper we find the conformable derivatives and integrals of needed function of radial basis functions (RBF) interpolation such as powers, Gaussians and multiquadric
Summary
We review the Riemann-Liouville fractional derivatives and integrals introduced in [3, 4, 23]. The left-sided Riemann-Liouville fractional derivative of order α of function u(t) is described as αDat u(t). The left-sided Riemann-Liouville fractional integral of order α of function u(t) is described as αIat u(t). Khalil et al [6] have introduced the conformable fractional derivative and integrals by following definition. The left sided conformable integral of u(t) of order α described by αItau(t) = tα−1u(t)dt, a t>a where α ∈ (0, 1) and the integral is classical integral operator. The right sided conformable integral of u(t) of order α described by b αIbt u(t) = (−t)α−1u(t)dt, t t
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