fractional derivative
A New Extension of Extended Caputo Fractional Derivative Operator
... the fractional derivative operator are found in many research ...Caputo fractional derivative ...tional derivative of some elementary functions derives by considering an extension of ...
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Analysis of the fractional diffusion equations with fractional derivative of non singular kernel
... multi-term fractional differential equations with the modified Riesz fractional derivative of Caputo type was introduced and employed in ...nonlinear fractional diffusion systems with the ...
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A New Truncated M-Fractional Derivative Type Unifying Some Fractional Derivative Types with Classical Properties
... -fractional derivative type satisfies the properties of the integer-order ...respective fractional integral from which emerges, as a natural consequence, the result, which can be interpreted as an ...
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FRACTIONAL NOETHER'S THEOREM WITH CLASSICAL AND GENERALIZED FRACTIONAL DERIVATIVE OPERATORS
... generalized fractional derivative operators, and derive a Noether type symme- try theorem to fractional problems of the calculus of variations with classical and generalized fractional ...
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On some applications of the space time fractional derivative
... one-dimensional fractional derivative to the multidimensional space-time fractional derivative, determine the exact solution via the Laplace transform, and develop mathematical foundations of ...
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A new construction of a fractional derivative mask for image edge analysis based on Riemann Liouville fractional derivative
... We have presented another way of constructing a fractional-based convolution mask for image edge analysis using the Riemann-Liouville fractional derivative formulation. Unlike other constructions, we ...
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On Generalized k-Fractional Derivative Operator
... k-fractional derivative op- erator by using the definition of k-beta ...defined fractional operator such as Mellin transform and relations to k- hypergeometric and k-Appell’s ...k-fractional ...
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Incomplete Caputo fractional derivative operators
... Caputo fractional derivative operators and show their use in the special function ...Caputo fractional derivative operators and show that the images of some elementary functions under the ...
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Weighted hypergeometric functions and fractional derivative
... where m – < Re μ < m, m ∈ N and u, v are real or complex parameters and τ is assumed to be a function of the class , i.e. such that the integral (.) is absolutely convergent. It is noted that (.) becomes the ...
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Two Definitions of Fractional Derivative of Powers Functions
... a fractional number ...tional derivative was attributed to Leibnitz and l’Hospital (1695) but significant developments on the subject were given later on by Riemann, Liouville, Grunwald-Letnikov and ...of ...
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On Extended Caputo Fractional Derivative Operator
... Caputo fractional derivative operator and they obtained many interesting results related to some familiar special functions by applying the said ...Caputo fractional derivative operator and ...
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Solving Fractional Derivative of Some Functions
... the fractional calculus is considered to be the Leibniz’s letter to L’Hospital in 1695, where the notation for differentiation of non‐integer order 1 2 is ...discussed. Fractional Calculus is one of the ...
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On an extension of Hadamard fractional derivative
... the fractional calculus in their fields [1, 9, 15, ...that fractional derivatives and integrals are more suitable for describing real ...of fractional calculus include fluid flow, dynamical processes in ...
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A posteriori error estimates for the fractional optimal control problems
... The purpose of this paper is to derive a posteriori error estimates for the FOCP gov- erned by the time fractional diffusion equation (TFDE) with Riemann-Liouville fractional derivative. Let = (–, ...
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Classical Properties on Conformable Fractional Calculus
... conformable fractional calculus involving fractional derivative and integral are ...conformable fractional derivative and fractional integral, mean value theorem and comparison ...
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Biorthogonal cubic Hermite spline multiwavelets on the interval for solving the fractional optimal control problems
... solving fractional optimal control problems (FOCPs) is presented. The fractional derivative in the dynamic system is described in the Caputo ...of fractional Riemann-Lioville integration and ...
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On Some Fractional-Integro Partial Differential Equations
... of fractional calculus are the ones of Riemann-Liouville and ...of fractional derivatives and integrals in engineering and science have been found in the past one hundred ...Caputo fractional ...
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Fractional Integral and Derivative of the 1/r Potential
... For mathematical properties of fractional derivatives and integrals one can consult [1]-[5] and the references therein. In this section we lay out the notation used in the next sec- tion as we consider the ...
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On boundary value problems of higher order abstract fractional integro-differential equations
... nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques such as fractional calculus, H¨ older inequality, Krasnoselskii’s fixed point ...
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Numerical solution of multi-order fractional differential equations via the sinc collocation method
... In this work, we apply the sinc collocation method for solving equation (1). The sinc method is an efficient method developed by Stenger [24]. It was widely used for the numerical solution of initial and boundary value ...
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