Journal of Fractional Calculus and Nonlinear Systems

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EISSN : 2709-9547
Published by: SABA Publishing (10.48185)
Total articles ≅ 22
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Amin Benaissa Cherif, Fatima Zohra Ladrani
Journal of Fractional Calculus and Nonlinear Systems, Volume 3, pp 12-19; https://doi.org/10.48185/jfcns.v3i1.391

Abstract:
We introduce more general concepts of nabla Riemann-Liouville fractional integrals and derivatives ontime scales. Such generalizations on time scales help us to study relations between fractional differenceequations and fractional differential equations. Sufficient conditions for the existence and uniqueness of thesolution to an initial value problem are described by nabla derivatives on time scales. Some properties of thenew operator are proved and illustrated with examples.
, Adnan Khan, Masaud Shah, Mubashir Khan
Journal of Fractional Calculus and Nonlinear Systems, Volume 3, pp 20-29; https://doi.org/10.48185/jfcns.v3i1.501

Abstract:
In this manuscript we have studied a five compartmental mathematical model of Ebola epidemic. Thesuggested mathematical model is classified into susceptible, incubation, infected, isolated infected and recoveredclasses. The Taylor series method (TSM) is used to achieve the approximate results for each compartment.The graphical presentation that corresponds to some real facts is given.
Journal of Fractional Calculus and Nonlinear Systems, Volume 3, pp 46-57; https://doi.org/10.48185/jfcns.v3i1.496

Abstract:
In the present work, the discrete homotopy analysis method is applied to solve nabla time-fractionalpartial difference equations. Fractional difference operator is considered in Caputo’s sense. We apply thediscrete homotopy analysis method to nabla fractional initial value problems. Obtained solutions involvean auxiliary parameter h, which we can determine. Thus, it may be concluded that the discrete homotopyanalysis method is a very powerful and successful analytical approach for fractional difference equations.
Journal of Fractional Calculus and Nonlinear Systems, Volume 3, pp 1-11; https://doi.org/10.48185/jfcns.v3i1.345

Abstract:
We study a class of fractional differential inclusions defined by Caputo-Katugampola fractional derivativeinvolving a nonconvex set-valued map in the presence of certain fractional integral boundary conditions.Using a technique developed by Filippov we establish an existence result for the problem considered underthe hypothesis that the set-valued map is Lipschitz in the state variable. Also, based on a result concerningthe arcwise connectedness of the fixed point set of a class of set-valued contractions, we prove the arcwiseconnectedness of the solution set of the problem considered. The paper is the first in literature which containssuch kind of results in the framework of the problem studied.
Naeem Ullah,
Journal of Fractional Calculus and Nonlinear Systems, Volume 3, pp 30-45; https://doi.org/10.48185/jfcns.v3i1.485

Abstract:
The main concern of the this article is to study the non-linear Chen-Lee-Liu equation which describes themotion of waves in shallow water. For this purpose two analytical techniques namely, the Sardar-Subequationmethod and the new extended hyperbolic function method are utilized. Also, we established the idea ofthe construction of solitons solutions of non-linear evolution equations which are rising in fluid dynamics,nonlinear optics, mathematical biological models, mechanics, waves theory, quantum mechanics. Acquiredsolutions are demonstrated graphically to reveal the dynamics behavior of solitons solutions. It hoped thatthe established solutions can be used to enrich the dynamic behaviors of Chen-Lee-Liu equation. Further,these solutions disclose that our techniques are up-to-date, suitable and straightforward.
Awais Younus, Muhammad Asif, Usama Atta, Tehmina Bashir,
Journal of Fractional Calculus and Nonlinear Systems, Volume 2, pp 13-30; https://doi.org/10.48185/jfcns.v2i2.342

Abstract:
In this paper, we provide the generalization of two predefined concepts under the name fuzzy conformable differential equations. We solve the fuzzy conformable ordinary differential equations under the strongly generalized conformable derivative. For the order $\Psi$, we use two methods. The first technique is to resolve a fuzzy conformable differential equation into two systems of differential equations according to the two types of derivatives. The second method solves fuzzy conformable differential equations of order $\Psi$ by a variation of the constant formula. Moreover, we generalize our results to solve fuzzy conformable ordinary differential equations of a higher order. Further, we provide some examples in each section for the sake of demonstration of our results.
Rajeev Kumar, Sanjeev Kumar, Sukhneet Kaur, Shrishty Jain
Journal of Fractional Calculus and Nonlinear Systems, Volume 2, pp 62-77; https://doi.org/10.48185/jfcns.v2i2.315

Abstract:
In this article, an attempt is made to achieve the series solution of the time fractional generalized Korteweg-de Vries equation which leads to a conditionally convergent series solution. We have also resorted to another technique involving conversion of the given fractional partial differential equations to ordinary differential equations by using fractional complex transform. This technique is discussed separately for modified Riemann-Liouville and conformable derivatives. Convergence analysis and graphical view of the obtained solution are demonstrated in this work.
Sabir Hussain, Sana Mehboob
Journal of Fractional Calculus and Nonlinear Systems, Volume 2, pp 93-112; https://doi.org/10.48185/jfcns.v2i2.390

Abstract:
The theory of fractional integral inequalities plays a pivotal role in approximation theory. It is very usefulin establishing the uniqueness of solutions for some fractional differential equations. Here, a generalizedfractional integral identity is established to deduce new estimates for Bullen type functional and of somerelated inequalities to provide some applications in probability and information theory for (s, p)−convexfunction by use of basic techniques of analysis.
Journal of Fractional Calculus and Nonlinear Systems, Volume 2, pp 78-92; https://doi.org/10.48185/jfcns.v2i2.353

Abstract:
In this paper, the existence of positive solutions of a class of nonlinear fractional boundary value problemsis considered. Two fixed point theorems are used, namely: Banach Contraction mapping principle andLeggett-Williams fixed point theorems. The former is used to prove the existence of a unique solution, whereasthe latter is used to prove the existence of at least three positive solutions to the problem. Some examples areprovided to illustrate the two results.
Awais Younus, Muhammad Asif, Usama Atta, Tehmina Bashir,
Journal of Fractional Calculus and Nonlinear Systems, Volume 2, pp 31-61; https://doi.org/10.48185/jfcns.v2i2.341

Abstract:
In this paper, we combine fuzzy calculus, and conformable calculus to introduce the fuzzy conformable calculus. We define the fuzzy conformable derivative of order $2\Psi $ and generalize it to derivatives of order $p\Psi $. Several properties on difference, product, sum, and addition of two fuzzy-valued functions are provided which are used in the solution of the fuzzy conformable differential equations. Also, examples in each case are given to illustrate the utility of our results.
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