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Annals of the West University of Timisoara: Mathematics and Computer Science, 2023 In this paper, we study the following fractional differential equation involving the Atangana-Baleanu-Caputo fractional derivative: {ABCaDτθ[x(ϑ)−F(ϑ,x(ϑ))]=G(ϑ,x(ϑ)), ϑ∈J:=[a,b],x(a)=φa∈ℝ.$$\left\{ {\matrix{ {AB{C_a}D_\tau ^\theta [x(\vartheta ...
Benkhettou Nadia +4 more
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On the mixed fractional quantum and Hadamard derivatives for impulsive boundary value problems
Open Mathematics, 2021 In this work, we initiate the study of a new class of impulsive boundary value problems consisting of mixed type fractional quantum and Hadamard derivatives.
Niyoom Somboon +3 more
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A comprehensive review on fractional-order optimal control problem and its solution
Open Mathematics, 2023 This article presents a comprehensive literature survey on fractional-order optimal control problems. Fractional-order differential equation is extensively used nowadays to model real-world systems accurately, which exhibit fractal dimensions, memory ...
Abd-Elmonem Assmaa +7 more
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Annales Mathematicae Silesianae, 2023 In this paper, we use the finite element method to solve the fractional space-time diffusion equation over finite fields. This equation is obtained from the standard diffusion equation by replacing the first temporal derivative with the new fractional ...
Boutiba Malika +2 more
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Pell-Lucas polynomials for numerical treatment of the nonlinear fractional-order Duffing equation
Demonstratio Mathematica, 2023 The nonlinear fractional-order cubic-quintic-heptic Duffing problem will be solved through a new numerical approximation technique. The suggested method is based on the Pell-Lucas polynomials’ operational matrix in the fractional and integer orders.
El-Sayed Adel Abd Elaziz
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On fractional kinetic equations k-Struve functions based solutions
Alexandria Engineering Journal, 2018 In the present research article, we investigate the solutions for fractional kinetic equations, involving k-Struve functions, some of the salient properties of which we present. The method used is Laplace transform based.
Kottakkaran Sooppy Nisar +2 more
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A new equivalence of Stefan's problems for the Time-Fractional-Diffusion Equation [PDF]
, 2014 A fractional Stefan problem with a boundary convective condition is solved, where the fractional derivative of order $ \alpha \in (0,1) $ is taken in the Caputo sense.
Marcus, Eduardo Santillan +1 more
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A note on fractional difference operators
Alexandria Engineering Journal, 2018 In the present article, following on very recent and new approach of fractional difference operator by Baliarsingh (2016), we establish some new ideas involving the exponent rules of this operator.
P. Baliarsingh, L. Nayak
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Fractional calculus of generalized p-k-Mittag-Leffler function using Marichev–Saigo–Maeda operators
Arab Journal of Mathematical Sciences, 2019 In this paper, we establish fractional integral and derivative formulas involving the generalized p-k-Mittag-Leffler function by using Marichev–Saigo–Maeda type fractional integral and derivative operators.
M. Kamarujjama, N.U. Khan, Owais Khan
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Fractional Sturm-Liouville eigenvalue problems, II [PDF]
, 2017 We continue the study of a non self-adjoint fractional three-term Sturm-Liouville boundary value problem (with a potential term) formed by the composition of a left Caputo and left-Riemann-Liouville fractional integral under {\it Dirichlet type} boundary
Dehghan, Mohammad, Mingarelli, Angelo B.
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