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Sotiris K. Ntouyas - One of the best experts on this subject based on the ideXlab platform.
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nonlinear sequential riemann liouville and caputo Fractional differential equations with generalized Fractional Integral conditions
Advances in Difference Equations, 2018Co-Authors: Chanon Promsakon, Sotiris K. Ntouyas, Nawapol Phuangthong, Jessada TariboonAbstract:In this paper, we discuss the existence and uniqueness of solutions for two new classes of sequential Fractional differential equations of Riemann–Liouville and Caputo types with generalized Fractional Integral boundary conditions, by using standard fixed point theorems. In addition, we also demonstrate the application of the obtained results with the aid of examples.
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Fractional differential equations involving generalized derivative with stieltjes and Fractional Integral boundary conditions
Applied Mathematics Letters, 2018Co-Authors: Bashir Ahmad, Sotiris K. Ntouyas, Madeaha Alghanmi, Ahmed AlsaediAbstract:Abstract In this paper, we obtain the sufficient conditions for the uniqueness of solutions for a boundary value problem of Fractional differential equations involving generalized Fractional derivative supplemented with Stieltjes and generalized Fractional Integral boundary conditions.
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positive solutions for Fractional differential systems with nonlocal riemann liouville Fractional Integral boundary conditions
Positivity, 2017Co-Authors: Khomsan Neamprem, Thanadon Muensawat, Sotiris K. Ntouyas, Jessada TariboonAbstract:In this paper, we study the positive solutions of Fractional differential system with coupled nonlocal Riemann–Liouville Fractional Integral boundary conditions. Our analysis relies on Leggett–Williams and Guo–Krasnoselskii’s fixed point theorems. Two examples are worked out to illustrate our main results.
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nonlocal hadamard Fractional Integral conditions and nonlinear riemann liouville Fractional differential equations and inclusions
2017Co-Authors: Bashir Ahmad, Sotiris K. Ntouyas, Ahmed Alsaedi, Jessada TariboonAbstract:In this chapter, we develop the existence theory for nonlocal boundary value problems of nonlinear Riemann-Liouville Fractional differential equations and inclusions supplemented with the Hadamard Fractional Integral boundary conditions. The key tool for the present study is the Property 2.25 from [96, p. 113] (see Lemma 1.6).
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on perturbed Fractional differential equations and inclusions with generalized riemann liouville Fractional Integral boundary conditions
International journal of pure and applied mathematics, 2016Co-Authors: Bashir Ahmad, Sotiris K. NtouyasAbstract:In this paper, we present the sufficient criteria for the existence of solutions for perturbed Fractional differential equations and inclusions with generalized Riemann-Liouville Fractional Integral boundary conditions. We make use of a nonlinear alternative, which deals with the sum of completely continuous and contractive single-valued or multi-valued operators, to obtain the desired results.
Jessada Tariboon - One of the best experts on this subject based on the ideXlab platform.
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nonlinear sequential riemann liouville and caputo Fractional differential equations with generalized Fractional Integral conditions
Advances in Difference Equations, 2018Co-Authors: Chanon Promsakon, Sotiris K. Ntouyas, Nawapol Phuangthong, Jessada TariboonAbstract:In this paper, we discuss the existence and uniqueness of solutions for two new classes of sequential Fractional differential equations of Riemann–Liouville and Caputo types with generalized Fractional Integral boundary conditions, by using standard fixed point theorems. In addition, we also demonstrate the application of the obtained results with the aid of examples.
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positive solutions for Fractional differential systems with nonlocal riemann liouville Fractional Integral boundary conditions
Positivity, 2017Co-Authors: Khomsan Neamprem, Thanadon Muensawat, Sotiris K. Ntouyas, Jessada TariboonAbstract:In this paper, we study the positive solutions of Fractional differential system with coupled nonlocal Riemann–Liouville Fractional Integral boundary conditions. Our analysis relies on Leggett–Williams and Guo–Krasnoselskii’s fixed point theorems. Two examples are worked out to illustrate our main results.
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nonlocal hadamard Fractional Integral conditions and nonlinear riemann liouville Fractional differential equations and inclusions
2017Co-Authors: Bashir Ahmad, Sotiris K. Ntouyas, Ahmed Alsaedi, Jessada TariboonAbstract:In this chapter, we develop the existence theory for nonlocal boundary value problems of nonlinear Riemann-Liouville Fractional differential equations and inclusions supplemented with the Hadamard Fractional Integral boundary conditions. The key tool for the present study is the Property 2.25 from [96, p. 113] (see Lemma 1.6).
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Positive solutions for Hadamard differential systems with Fractional Integral conditions on an unbounded domain
De Gruyter, 2017Co-Authors: Jessada Tariboon, Ntouyas Sotiris K., Asawasamrit Suphawat, Promsakon ChanonAbstract:In this paper, we investigate the existence of positive solutions for Hadamard type Fractional differential system with coupled nonlocal Fractional Integral boundary conditions on an infinite domain. Our analysis relies on Guo-Krasnoselskii’s and Leggett-Williams fixed point theorems. The obtained results are well illustrated with the aid of examples
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boundary value problems for riemann liouville Fractional differential inclusions with nonlocal hadamard Fractional Integral conditions
Mediterranean Journal of Mathematics, 2016Co-Authors: Sotiris K. Ntouyas, Jessada Tariboon, Weerawat SudsutadAbstract:In this paper, we study a new class of boundary value problems from a Fractional differential inclusion of Riemann–Liouville type and nonlocal Hadamard Fractional Integral boundary conditions. Some new existence results for convex as well as non-convex multi-valued maps are obtained using standard fixed point theorems. The obtained results are illustrated by examples.
Ghulam Farid - One of the best experts on this subject based on the ideXlab platform.
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study of a generalized riemann liouville Fractional Integral via convex functions
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 2020Co-Authors: Ghulam FaridAbstract:In this paper estimations in general form of sum of left and right sided Riemann-Liouville (RL) Fractional Integrals for convex functions are studied. Also some similar Fractional inequalities for functions whose deriva tives in absolute value are convex, have been obtained. Associated Fractional Integral inequalities provide the bounds of different known Fractional inequal ities. These results may be useful in in the study of uniqueness solutions of Fractional differential equations and Fractional boundary value problems.
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boundedness of Fractional Integral operators containing mittag leffler function via exponentially s convex functions
Journal of Mathematics, 2020Co-Authors: Gang Hong, Ghulam Farid, Waqas Nazeer, Saira Bano Akbar, J Pecaric, Shengtao GengAbstract:The main objective of this paper is to obtain the Fractional Integral operator inequalities which provide bounds of the sum of these operators at an arbitrary point. These inequalities are derived for - exponentially convex functions. Furthermore, a Hadamard inequality is obtained for Fractional Integrals by using exponentially symmetric functions. The results of this paper contain several such consequences for known Fractional Integrals and functions which are convex, exponentially convex, and - convex.
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some riemann liouville Fractional Integral inequalities for convex functions
The Journal of Analysis, 2019Co-Authors: Ghulam FaridAbstract:We are pleased to investigate some Riemann–Liouville Fractional Integral inequalities in a very simple and novel way. By using convexity of a function f and a simple inequality over the domain of f we establish some interesting results.
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Fractional Integral inequalities of gruss type via generalized mittag leffler function
International Journal of Analysis and Applications, 2019Co-Authors: Ghulam Farid, Vishnu Narayan Mishra, Atiq Ur Rehman, S MehmoodAbstract:We use generalized Fractional Integral operator containing the generalized Mittag-Leffler function to establish some new Integral inequalities of Gr¨uss type. A cluster of Fractional Integral inequalities have been identified by setting particular values to parameters involved in the Mittag-Leffler special function. Presented results contain several Fractional Integral inequalities which reflects their importance.
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a generalized fejer hadamard inequality for harmonically convex functions via generalized Fractional Integral operator and related results
Mathematics, 2018Co-Authors: Shin Min Kang, Ghulam Farid, Ghulam Abbas, Waqas NazeerAbstract:In this paper, we obtain a version of the Fejer–Hadamard inequality for harmonically convex functions via generalized Fractional Integral operator. In addition, we establish an Integral identity and some Fejer–Hadamard type Integral inequalities for harmonically convex functions via a generalized Fractional Integral operator. Being generalizations, our results reproduce some known results.
Delfim F M Torres - One of the best experts on this subject based on the ideXlab platform.
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direct transcription methods based on Fractional Integral approximation formulas for solving nonlinear Fractional optimal control problems
Communications in Nonlinear Science and Numerical Simulation, 2019Co-Authors: Abubakar Bello Salati, M Shamsi, Delfim F M TorresAbstract:Abstract This paper presents three direct methods based on Grunwald–Letnikov, trapezoidal and Simpson Fractional Integral formulas to solve Fractional optimal control problems (FOCPs). At first, the Fractional Integral form of FOCP is considered, then the Fractional Integral is approximated by Grunwald–Letnikov, trapezoidal and Simpson formulas in a matrix approach. Thereafter, the performance index is approximated either by trapezoidal or Simpson quadrature. As a result, FOCPs are reduced to nonlinear programming problems, which can be solved by many well-developed algorithms. To improve the efficiency of the presented method, the gradient of the objective function and the Jacobian of constraints are prepared in closed forms. It is pointed out that the implementation of the methods is simple and, due to the fact that there is no need to derive necessary conditions, the methods can be simply and quickly used to solve a wide class of FOCPs. The efficiency and reliability of the presented methods are assessed by ample numerical tests involving a free final time with path constraint FOCP, a bang-bang FOCP and an optimal control of a Fractional-order HIV-immune system.
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expansion formulas in terms of integer order derivatives for the hadamard Fractional Integral and derivative
Numerical Functional Analysis and Optimization, 2012Co-Authors: Shakoor Pooseh, Ricardo Almeida, Delfim F M TorresAbstract:We obtain series expansion formulas for the Hadamard Fractional Integral and Fractional derivative of a smooth function. When considering finite sums only, an upper bound for the error is given. Numerical simulations show the efficiency of the approximation method.
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Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics
Abstract and Applied Analysis, 2012Co-Authors: Tatiana Odzijewicz, Agnieszka B. Malinowska, Delfim F M TorresAbstract:We study Fractional variational problems in terms of a generalized Fractional Integral with Lagrangians depending on classical derivatives, generalized Fractional Integrals and derivatives. We obtain necessary optimality conditions for the basic and isoperimetric problems, as well as natural boundary conditions for free boundary value problems. The Fractional action-like variational approach (FALVA) is extended and some applications to Physics discussed.
Praveen Agarwal - One of the best experts on this subject based on the ideXlab platform.
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Fractional Integral operators involving extended mittag leffler function as its kernel
Boletin De La Sociedad Matematica Mexicana, 2018Co-Authors: Gauhar Rahman, Shahid Mubeen, Praveen Agarwal, Muhammad ArshadAbstract:This paper is devoted to the study of Fractional calculus with an Integral and differential operators containing the following family of extended Mittag–Leffler function: $$\begin{aligned} E_{\alpha ,\beta }^{\gamma ;c}(z; p)=\sum \limits _{n=0}^{\infty }\frac{B_p(\gamma +n, c-\gamma )(c)_{n}}{B(\gamma , c-\gamma )\Gamma (\alpha n+\beta )}\frac{z^n}{n!}, (z,\beta , \gamma \in \mathbb {C}), \end{aligned}$$ in its kernel. Also, we further introduce a certain number of consequences of Fractional Integral and differential operators containing the said function in their kernels.
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pathway Fractional Integral operator associated with 3m parametric mittag leffler functions
International Journal of Applied and Computational Mathematics, 2018Co-Authors: Shilpi Jain, Praveen Agarwal, Adem KilicmanAbstract:In this paper, we present composition of the pathway Fractional Integral $$P_{0^{+} }^{(\eta ,\alpha )}$$ with the 3m-parametric type Mittag-Leffler function $$E^{(\gamma _{i}),m}_{(\alpha _i), (\beta _i)}(z)$$ and discusses some of it’s particular cases in application point of view.
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some generalized riemann liouville k Fractional Integral inequalities
Journal of Inequalities and Applications, 2016Co-Authors: Praveen Agarwal, Sotiris K. Ntouyas, Jessada TariboonAbstract:The focus of the present study is to prove some new Polya-Szego type Integral inequalities involving the generalized Riemann-Liouville k-Fractional Integral operator. These inequalities are used then to establish some Fractional Integral inequalities of Chebyshev type.
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certain inequalities involving the Fractional Integral operators
Abstract and Applied Analysis, 2014Co-Authors: Dumitru Baleanu, Praveen AgarwalAbstract:We establish some inequalities involving Saigo Fractional -Integral operator in the theory of quantum calculus by using the two parameters of deformation, and , whose special cases are shown to yield corresponding inequalities associated with Riemann-Liouville and Kober Fractional -Integral operators, respectively. Furthermore, we also consider their relevance with other related known results.
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certain gruss type inequalities involving the generalized Fractional Integral operator
Journal of Inequalities and Applications, 2014Co-Authors: Guotao Wang, Praveen Agarwal, Mehar ChandAbstract:A remarkably large number of Gruss type Fractional Integral inequalities involving the special function have been investigated by many authors. Very recently, Kalla and Rao (Matematiche LXVI(1):57-64, 2011) gave two Gruss type inequalities involving the Saigo Fractional Integral operator. Using the same technique, in this paper, we establish certain new Gruss type Fractional Integral inequalities involving the Gauss hypergeometric function. Moreover, we also consider their relevances for other related known results.
