Journal ArticleDOI
Non-local fractional calculus from different viewpoint generated by truncated M-derivative
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TLDR
This paper proposes more favored novel non-local fractional integral and derivative operators with three parameters by using the iteration manner on truncated M -derivative involving truncated Mittag-Leffler function to solve Sturm–Liouville problem subjected to the initial conditions.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2020-03-01. It has received 36 citations till now. The article focuses on the topics: Fractional calculus & Laplace transform.read more
Citations
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Journal ArticleDOI
New Illustrative Applications of Integral Transforms to Financial Models with Different Fractional Derivatives
TL;DR: The efficiency and accuracy of the Sumudu transform and decomposition series method constructed by the Laplace transform is proved in providing the solutions of several different linear/nonlinear financial models by considering the theoretical results and illustrative applications.
Journal ArticleDOI
Mathematical modeling of pine wilt disease with Caputo fractional operator
TL;DR: In this article, the authors investigated the transmission dynamics of pine wilt disease infection and developed a new model utilizing Caputo fractional-order derivative, and with the use of fixed point theorem, they obtained the existence and uniqueness of the pine Wilt disease model are obtained under Caputo operator.
Journal ArticleDOI
Analysis of an Epidemic Spreading Model with Exponential Decay Law
Mehmet Yavuz,Necati Özdemir +1 more
TL;DR: In this article, a SIR model that categorizes individuals in a population as susceptible (S), infected (I) and recovered (R) was used to simulate the transmission dynamics of diseases where individuals acquire permanent immunity.
Journal ArticleDOI
Optical solitons with M-truncated and beta derivatives in nonlinear optics
Abdullahi Yusuf,Dumitru Baleanu +1 more
TL;DR: In this article, two well-known integration schemes which are generalized tanh method (GTM) and generalized Bernoulli sub-ODE method (GBM) are utilized to extract such optical soliton solutions.
Journal ArticleDOI
On explicit wave solutions of the fractional nonlinear dsw system via the modified khater method
Chen Yue,Dianchen Lu,Mostafa M. A. Khater,Abdel-Haleem Abdel-Aty,W. Alharbi,Raghda A. M. Attia,Raghda A. M. Attia +6 more
TL;DR: In this paper, the exact traveling and solitary wave solutions of the fractional nonlinear Drinfeld-Sokolov-Wilson (DSW) system were obtained by employing the modified Khater (mK) method through a n...
References
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Journal ArticleDOI
A new definition of fractional derivative
TL;DR: A new definition of fractional derivative and fractional integral is given and it is shown that it is the most natural definition, and the most fruitful one.
Journal ArticleDOI
On conformable fractional calculus
TL;DR: The basic concepts in this new simple interesting fractional calculus called conformable fractional derivative are set and the fractional versions of chain rule, exponential functions, Gronwall's inequality, integration by parts, Taylor power series expansions, Laplace transforms and linear differential systems are proposed and discussed.
Journal ArticleDOI
New approach to a generalized fractional integral
TL;DR: A new fractional integration is presented, which generalizes the Riemann–Liouville and Hadamard fractional integrals into a single form andSemigroup property for the above operator is proved.
Journal ArticleDOI
On the ψ-Hilfer fractional derivative
TL;DR: In this article, a new fractional derivative with respect to another function is introduced, the so-called ψ-Hilfer fractional derivatives, which can be used to obtain uniformly convergent sequence of function, uniformly continuous function and examples including the Mittag-Leffler function with one parameter.
Journal ArticleDOI
On a new class of fractional operators
TL;DR: In this paper, the authors introduce new fractional integration and differentiation operators based on the standard fractional calculus iteration procedure on conformable derivatives and define spaces and present some theorems related to these operators.
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