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  • 2015-2019  (47)
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  • 1
    Online Resource
    Online Resource
    London : IntechOpen
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource
    ISBN: 9781839626593 , 9781839626609
    URL: Volltext  (kostenfrei)
    Language: English
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  • 2
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    MDPI Publishing
    In: Entropy
    Publication Date: 2017-12-20
    Description: Entropy, Vol. 19, Pages 681: Chaos in a Cancer Model via Fractional Derivatives with Exponential Decay and Mittag-Leffler Law Entropy doi: 10.3390/e19120681 Authors: José Gómez-Aguilar María López-López Victor Alvarado-Martínez Dumitru Baleanu Hasib Khan In this paper, a three-dimensional cancer model was considered using the Caputo-Fabrizio-Caputo and the new fractional derivative with Mittag-Leffler kernel in Liouville-Caputo sense. Special solutions using an iterative scheme via Laplace transform, Sumudu-Picard integration method and Adams-Moulton rule were obtained. We studied the uniqueness and existence of the solutions. Novel chaotic attractors with total order less than three are obtained.
    Electronic ISSN: 1099-4300
    Topics: Chemistry and Pharmacology , Physics
    Published by MDPI Publishing
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  • 3
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    MDPI Publishing
    In: Entropy
    Publication Date: 2017-07-23
    Description: Entropy, Vol. 19, Pages 375: A Novel Numerical Approach for a Nonlinear Fractional Dynamical Model of Interpersonal and Romantic Relationships Entropy doi: 10.3390/e19070375 Authors: Jagdev Singh Devendra Kumar Maysaa Al Qurashi Dumitru Baleanu In this paper, we propose a new numerical algorithm, namely q-homotopy analysis Sumudu transform method (q-HASTM), to obtain the approximate solution for the nonlinear fractional dynamical model of interpersonal and romantic relationships. The suggested algorithm examines the dynamics of love affairs between couples. The q-HASTM is a creative combination of Sumudu transform technique, q-homotopy analysis method and homotopy polynomials that makes the calculation very easy. To compare the results obtained by using q-HASTM, we solve the same nonlinear problem by Adomian’s decomposition method (ADM). The convergence of the q-HASTM series solution for the model is adapted and controlled by auxiliary parameter and asymptotic parameter n. The numerical results are demonstrated graphically and in tabular form. The result obtained by employing the proposed scheme reveals that the approach is very accurate, effective, flexible, simple to apply and computationally very nice.
    Electronic ISSN: 1099-4300
    Topics: Chemistry and Pharmacology , Physics
    Published by MDPI Publishing
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  • 4
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    SpringerOpen
    Publication Date: 2017-03-25
    Description: The key purpose of the present work is to examine a fractional giving up smoking model pertaining to a new fractional derivative with non-singular kernel. The numerical simulations are conducted with the aid o...
    Print ISSN: 1687-1839
    Electronic ISSN: 1687-1847
    Topics: Mathematics
    Published by SpringerOpen
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  • 5
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    MDPI Publishing
    In: Entropy
    Publication Date: 2017-06-23
    Description: In this paper, we propose a new type (n + 1)-dimensional reduced differential transform method (RDTM) based on a local fractional derivative (LFD) to solve (n + 1)-dimensional local fractional partial differential equations (PDEs) in Cantor sets. The presented method is named the (n + 1)-dimensional local fractional reduced differential transform method (LFRDTM). First the theories, their proofs and also some basic properties of this procedure are given. To understand the introduced method clearly, we apply it on the (n + 1)-dimensional fractal heat-like equations (HLEs) and wave-like equations (WLEs). The applications show that this new technique is efficient, simply applicable and has powerful effects in (n + 1)-dimensional local fractional problems.
    Electronic ISSN: 1099-4300
    Topics: Chemistry and Pharmacology , Physics
    Published by MDPI Publishing
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  • 6
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    SpringerOpen
    Publication Date: 2017-07-08
    Description: In this note we present some corrections to our previous paper (Nisar et al. in Adv. Differ. Equ. 2017:118, 2017).
    Print ISSN: 1687-1839
    Electronic ISSN: 1687-1847
    Topics: Mathematics
    Published by SpringerOpen
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  • 7
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    SpringerOpen
    Publication Date: 2015-08-07
    Description: In this paper, we discussed the existence of solutions for the fractional finite difference inclusion Δ ν x ( t ) ∈ F ( t , x ( t ) , Δ x ( t ) , Δ 2 x ( t ) ) via the boundary value conditions ξ x ( ν − 3 ) + β Δ x ( ν − 3 ) = 0 , x ( η ) = 0 , and γ x ( b + ν ) + δ Δ x ( b + ν ) = 0 , where η ∈ N ν − 2 b + ν − 1 , 2 〈 ν 〈 3 , and F : N ν − 3 b + ν + 1 × R × R × R → 2 R is a compact valued multifunction.
    Print ISSN: 1687-1839
    Electronic ISSN: 1687-1847
    Topics: Mathematics
    Published by SpringerOpen
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  • 8
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    SpringerOpen
    Publication Date: 2015-07-17
    Description: In this work, we study the fractional order Lane-Emden differential equations by using the reproducing kernel method. The exact solution is shown in the form of a series in the reproducing kernel Hilbert space. Some numerical examples are given in order to demonstrate the accuracy of the present method. The results obtained from the method are compared with the exact solutions and another method. The obtained numerical results are better than the ones provided by the collocation method. Results of numerical examples show that the presented method is simple, effective, and easy to use.
    Print ISSN: 1687-1839
    Electronic ISSN: 1687-1847
    Topics: Mathematics
    Published by SpringerOpen
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  • 9
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    MDPI Publishing
    In: Entropy
    Publication Date: 2015-02-17
    Description: In this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann–Liouville) or a solution with increasing length of their support (Hukuhara difference). Then, in order to solve the FFDE analytically, we introduce the fuzzy Laplace transform of the Caputo H-derivative. To the best of our knowledge, there is limited research devoted to the analytical methods to solve the FFDE under the fuzzy Caputo fractional differentiability. An analytical solution is presented to confirm the capability of the proposed method.
    Electronic ISSN: 1099-4300
    Topics: Chemistry and Pharmacology , Physics
    Published by MDPI Publishing
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  • 10
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    SpringerOpen
    Publication Date: 2017-02-11
    Description: We present a new method to investigate some fractional integro-differential equations involving the Caputo-Fabrizio derivation and we prove the existence of approximate solutions for these problems. We provide...
    Print ISSN: 1687-1839
    Electronic ISSN: 1687-1847
    Topics: Mathematics
    Published by SpringerOpen
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