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Dumitru Baleanu - One of the best experts on this subject based on the ideXlab platform.
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on the solutions of certain fractional kinetic equations involving k mittag Leffler Function
Advances in Difference Equations, 2018Co-Authors: Praveen Agarwal, Dumitru Baleanu, Mehar Chand, Donal Oregan, Shilpi JainAbstract:The aim of the present paper is to develop a new generalized form of the fractional kinetic equation involving a generalized k-Mittag-Leffler Function \(E^{\gamma,\rho}_{k,\zeta,\eta}(\cdot)\). The solutions of fractional kinetic equations are discussed in terms of the Mittag-Leffler Function. Further, numerical values of the results and their graphical interpretation is interpreted to study the behavior of these solutions. The results established here are quite general in nature and capable of yielding both known and new results.
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the k s k s fractional calculus of k mittag Leffler Function
Advances in Difference Equations, 2017Co-Authors: Kottakkaran Sooppy Nisar, Dumitru Baleanu, Gauhar Rahman, Shahid Mubeen, Muhammad ArshadAbstract:In this paper, we introduce the $(k, s)$ -fractional integral and differential operators involving k-Mittag-Leffler Function $E_{k,\rho,\beta}^{\delta}(z)$ as its kernel. Also, we establish various properties of these operators. Further, we consider a number of certain consequences of the main results.
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Measurement of para-xylene diffusivity in zeolites and analyzing desorption curves using the Mittag-Leffler Function
Fractional Calculus and Applied Analysis, 2016Co-Authors: Sharif F. Zaman, Dumitru Baleanu, Ivo PetrasAbstract:AbstractThe new fractional calculus modeling based on Mittag-Leffler Function has been employed to generate a better fit model to analyze the ZLC desorption curves for para-xylene diffusion in ZSM-5 zeolites. The diffusivity values generated herewith at 100, 125 and 150°C are reported as 4.4×10
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mittag Leffler Function for discrete fractional modelling
Journal of King Saud University - Science, 2016Co-Authors: Guocheng Wu, Dumitru Baleanu, Shengda ZengAbstract:Abstract From the difference equations on discrete time scales, this paper numerically investigates one discrete fractional difference equation in the Caputo delta’s sense which has an explicit solution in form of the discrete Mittag-Leffler Function. The exact numerical values of the solutions are given in comparison with the truncated Mittag-Leffler Function.
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a generalized q mittag Leffler Function by q captuo fractional linear equations
Abstract and Applied Analysis, 2012Co-Authors: Thabet Abdeljawad, Betül Benli, Dumitru BaleanuAbstract:Some Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler Functions. The method of successive approximation is used to obtain the solutions. The obtained q-version of Mittag-Leffler Function is thought as the q-analogue of the one introduced previously by Kilbas and Saigo (1995).
Rozana Liko - One of the best experts on this subject based on the ideXlab platform.
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Fractional integral inequalities for generalized- $$\mathbf{m }$$ m -
Arabian Journal of Mathematics, 2020Co-Authors: Gerasimos Anastassiou, Artion Kashuri, Rozana LikoAbstract:The authors discover a new identity concerning differentiable mappings defined on $$\mathbf{m }$$ m -invex set via general fractional integrals. Using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized- $$\mathbf{m }$$ m - $$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) -convex mappings by involving an extended generalized Mittag–Leffler Function are presented. It is pointed out that some new special cases can be deduced from main results. Also these inequalities have some connections with known integral inequalities. At the end, some applications to special means for different positive real numbers are provided as well.
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Fractional integral inequalities for generalized-$$\mathbf{m }$$m-$$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$((h1p,h2q);(η1,η2))-convex mappings via an extended generalized Mittag–Leffler Function
Arabian Journal of Mathematics, 2019Co-Authors: Gerasimos Anastassiou, Artion Kashuri, Rozana LikoAbstract:The authors discover a new identity concerning differentiable mappings defined on $$\mathbf{m }$$ m -invex set via general fractional integrals. Using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized- $$\mathbf{m }$$ m - $$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) -convex mappings by involving an extended generalized Mittag–Leffler Function are presented. It is pointed out that some new special cases can be deduced from main results. Also these inequalities have some connections with known integral inequalities. At the end, some applications to special means for different positive real numbers are provided as well.
Gerasimos Anastassiou - One of the best experts on this subject based on the ideXlab platform.
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Fractional integral inequalities for generalized- $$\mathbf{m }$$ m -
Arabian Journal of Mathematics, 2020Co-Authors: Gerasimos Anastassiou, Artion Kashuri, Rozana LikoAbstract:The authors discover a new identity concerning differentiable mappings defined on $$\mathbf{m }$$ m -invex set via general fractional integrals. Using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized- $$\mathbf{m }$$ m - $$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) -convex mappings by involving an extended generalized Mittag–Leffler Function are presented. It is pointed out that some new special cases can be deduced from main results. Also these inequalities have some connections with known integral inequalities. At the end, some applications to special means for different positive real numbers are provided as well.
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Fractional integral inequalities for generalized-$$\mathbf{m }$$m-$$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$((h1p,h2q);(η1,η2))-convex mappings via an extended generalized Mittag–Leffler Function
Arabian Journal of Mathematics, 2019Co-Authors: Gerasimos Anastassiou, Artion Kashuri, Rozana LikoAbstract:The authors discover a new identity concerning differentiable mappings defined on $$\mathbf{m }$$ m -invex set via general fractional integrals. Using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized- $$\mathbf{m }$$ m - $$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) -convex mappings by involving an extended generalized Mittag–Leffler Function are presented. It is pointed out that some new special cases can be deduced from main results. Also these inequalities have some connections with known integral inequalities. At the end, some applications to special means for different positive real numbers are provided as well.
Thabet Abdeljawad - One of the best experts on this subject based on the ideXlab platform.
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a generalized q mittag Leffler Function by q captuo fractional linear equations
Abstract and Applied Analysis, 2012Co-Authors: Thabet Abdeljawad, Betül Benli, Dumitru BaleanuAbstract:Some Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler Functions. The method of successive approximation is used to obtain the solutions. The obtained q-version of Mittag-Leffler Function is thought as the q-analogue of the one introduced previously by Kilbas and Saigo (1995).
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caputo q fractional initial value problems and a q analogue mittag Leffler Function
Communications in Nonlinear Science and Numerical Simulation, 2011Co-Authors: Thabet Abdeljawad, Dumitru BaleanuAbstract:Abstract Caputo q-fractional derivatives are introduced and studied. A Caputo -type q-fractional initial value problem is solved and its solution is expressed by means of a new introduced q-Mittag–Leffler Function. Some open problems about q-fractional integrals are proposed as well.
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A Quantum Generalized Mittag-Leffler Function Via Caputo q-Fractional Equations
arXiv: Dynamical Systems, 2011Co-Authors: Thabet Abdeljawad, Betül BenliAbstract:Some Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler Functions. The method of successive approximation is used to obtain the solutions. The obtained q-version of Mittag-Leffler Function is thought as the q-analogue of the one introduced previously by Kilbas and Saigo. AMS Subject Classification: 26A33; 60G05; 60G07; 60G012; 60GH05,41A05, 33D60, 34G10.
Edmundo Capelas De Oliveira - One of the best experts on this subject based on the ideXlab platform.
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integral representations of mittag Leffler Function on the positive real axis
TEMA - Tendências em Matemática Aplicada e Computacional, 2019Co-Authors: Eliana Contharteze Grigoletto, Edmundo Capelas De Oliveira, Rubens De Figueiredo CamargoAbstract:The Mittag-Leffler Functions appear in many problems associated with fractional calculus. In this paper, we use the methodology for evaluation of the inverse Laplace transform, proposed by M. N. Berberan-Santos, to show that the three-parameter Mittag-Leffler Function has similar integral representations on the positive real axis. Some of the integrals are also presented.
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three parameter mittag Leffler Function with an integral representation on the positive real axis
Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 2018Co-Authors: Eliana Contharteze Grigoletto, Rubens De Figueiredo Camargo, Edmundo Capelas De OliveiraAbstract:In this paper, we use the methodology for evaluation of the inverse Laplace transform, proposed by M. N. Berberan-Santos, to show that the three-parameter Mittag-Leffler Function has an integral representation on the positive real axis. Some of integrals are also presented.
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On the Generalized Mittag-Leffler Function and its Application in a Fractional Telegraph Equation
Mathematical Physics Analysis and Geometry, 2012Co-Authors: Rubens Figueiredo Camargo, Edmundo Capelas De OliveiraAbstract:The classical Mittag-Leffler Functions, involving one- and two-parameter, play an important role in the study of fractional-order differential (and integral) equations. The so-called generalized Mittag-Leffler Function, a Function with three-parameter which generalizes the classical ones, appear in the fractional telegraph equation. Here we introduce some integral transforms associated with this generalized Mittag-Leffler Function. As particular cases some recent results are recovered.