Browsing by Author "Agarwal, Ravi P."

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Citation Count: Baleanu, Dumitru; Agarwal, P., "A Composition Formula of the Pathway Integral Transform Operator", Note di Matematica, Vol. 34, No. 2, pp. 145-155, (2014).
A Composition Formula of the Pathway Integral Transform Operator
(University of Salento, 2014) Baleanu, Dumitru; Agarwal, Ravi P.; 56389
In the present paper, we aim at presenting composition formula of integral transform operator due to Nair, which is expressed in terms of the generalized Wright hypergeometric function, by inserting the generalized Bessel function of the first kind wv(z). Furthermore the special cases for the product of trigonometric functions are also consider. © 2014 Universitá del Salento.
Citation Count: Agarwal, Ritu; Jain, Sonal; Agarwal, Ravi P.; et al. (2018). A Remark on the Fractional Integral Operators and the Image Formulas of Generalized Lommel-Wright Function, Frontiers in Physics, 6.
A Remark on the Fractional Integral Operators and the Image Formulas of Generalized Lommel-Wright Function
(Frontiers Media S.A., 2018) Agarwal, Ritu; Jain, Sonal; Agarwal, Ravi P.; Baleanu, Dumitru; 56389
In this paper, the operators of fractional integration introduced by Marichev-Saigo-Maeda involving Appell's function F-3(center dot) are applied, and several new image formulas of generalized Lommel-Wright function are established. Also, by implementing some integral transforms on the resulting formulas, few more image formulas have been presented. We can conclude that all derived results in our work generalize numerous well-known results and are capable of yielding a number of applications in the theory of special functions.
Citation Count: Agarwal, Ravi P...et al. (2018). "A survey on fuzzy fractional differential and optimal control nonlocal evolution equations", Journal of Computational and Applied Mathematics, Vol. 339, pp.. 3-29.
A survey on fuzzy fractional differential and optimal control nonlocal evolution equations
(Elsevier, 2018) Agarwal, Ravi P.; Baleanu, Dumitru; Nieto, Juan J.; Torres, Delfim F. M.; Zhou, Yong; 56389
We survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution equations. Optimality and relaxation of multiple control problems, described by nonlinear fractional differential equations with nonlocal control conditions in Banach spaces, are considered. (C) 2017 Elsevier B.V. All rights reserved.
Citation Count: Karapınar, Erdal; Fulga, Andreea; Agarwal, Ravi P. (2020). "A survey:F-contractions with related fixed point results", Journal of Fixed Point Theory and Applications, Vol. 22, No. 3.
A survey:F-contractions with related fixed point results
(2020) Karapınar, Erdal; Fulga, Andreea; Agarwal, Ravi P.; 19184
In this note, we aim to review the recent results onF-contractions, introduced by Wardowski. After examining the fixed point results for such operators, we collect the sequent results in this direction in a different setting. One of the aims of this survey is to provide a complete collection of several fixed generalizations and extensions ofF-contractions.
Citation Count: Baleanu, D., Mustafa, O.G., Agarwal, R.P. (2010). An existence result for a superlinear fractional differential equation. Applied Mathematics Letters, 23(9), 1129-1132. http://dx.doi.org/10.1016/j.aml.2010.04.049
An existence result for a superlinear fractional differential equation
(Pergamon-Elsevier Science Ltd, 2010) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.
We establish the existence and uniqueness of solution for the boundary value problem (0)D(t)(alpha)(x') + a(t)x(lambda) = 0, t > 0, x' (0) = 0, lim(t ->+infinity) x(t) = 1, where (0)D(t)(alpha) designates the Riemann-Liouville derivative of order alpha epsilon (0, 1) and lambda > 1. Our result might be useful for establishing a non-integer variant of the Atkinson classical theorem on the oscillation of Emden-Fowler equations
Citation Count: Bleanu, D.; Mustafa, O.G.; Agarwal, R.P.,"Asymptotic Integration of (1 + Α) -Order Fractional Differential Equations",Vol. 62, No. 3, pp. 1492-1500, (2011).
Asymptotic Integration of (1 + Α) -Order Fractional Differential Equations
(2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.; 56389
We establish the long-time asymptotic formula of solutions to the (1+α)-order fractional differential equation 0iOt1+αx+a(t)x=0, t>0, under some simple restrictions on the functional coefficient a(t), where 0iOt1+α is one of the fractional differential operators 0Dtα(x′), (0Dtαx)′= 0Dt1+αx and 0Dtα(tx′-x). Here, 0Dtα designates the Riemann-Liouville derivative of order α∈(0,1). The asymptotic formula reads as [b+O(1)] ·xsmall+c·xlarge as t→+∞ for given b, c∈R, where xsmall and xlarge represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation 0iOt1+αx=0, t>0
Citation Count: Baleanu, D...et al. (2011). Asymptotic integration of (1+alpha)-order fractional differential equations. Computers&Mathematics With Applications, 62(3), 1492-1500. http://dx.doi.org/10.1016/j.camwa.2011.03.021
Asymptotic integration of (1+alpha)-order fractional differential equations
(Pergamon-Elsevier Science Ltd, 2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.
We establish the long-time asymptotic formula of solutions to the (1 + alpha)-order fractional differential equation (i)(0)O(t)(1+alpha)x + a (t)x = 0, t > 0, under some simple restrictions on the functional coefficient a(t), where (i)(0)O(t)(1+alpha)x is one of the fractional differential operators D-0(t)alpha(x'), ((0)D(t)(alpha)x)' = D-0(t)1+alpha x and D-0(t)alpha(tx' - x). Here, D-0(t)alpha designates the Riemann-Liouville derivative of order a E (0, 1). The asymptotic formula reads as [b + O(1)] . x(small) + c . x(large) as t -> +infinity for given b, c E is an element of R, where x(small) and x(large) represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation (i)(0)O(t)(1+alpha)x = 0, t > 0.
Citation Count: Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P. " Asymptotic integration of (1+alpha)-order fractional differential equations", Computers & Mathematics With Applications, Vol. 62, No. 3, pp. 1492-1500, (2011)
Asymptotic Integration of (1+Alpha)-Order Fractional Differential Equations
(Pergamon-Elsevier Science LTD, 2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.; 56389
We establish the long-time asymptotic formula of solutions to the (1 + alpha)-order fractional differential equation (i)(0)O(t)(1+alpha)x + a (t)x = 0, t > 0, under some simple restrictions on the functional coefficient a(t), where (i)(0)O(t)(1+alpha)x is one of the fractional differential operators D-0(t)alpha(x'), ((0)D(t)(alpha)x)' = D-0(t)1+alpha x and D-0(t)alpha(tx' - x). Here, D-0(t)alpha designates the Riemann-Liouville derivative of order a E (0, 1). The asymptotic formula reads as [b + O(1)] . x(small) + c . x(large) as t -> +infinity for given b, c E is an element of R, where x(small) and x(large) represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation (i)(0)O(t)(1+alpha)x = 0, t > 0. (C) 2011 Elsevier Ltd. All rights reserved.
Citation Count: Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P. (2011). "Asymptotic integration of (1+alpha)-order fractional differential equations", Computers & Mathematics With Applications, Vol. 62, no. 3, pp. 1492-1500.
Asymptotic integration of (1+alpha)-order fractional differential equations
(2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.; 56389
We establish the long-time asymptotic formula of solutions to the (1 + alpha)-order fractional differential equation (i)(0)O(t)(1+alpha)x + a (t)x = 0, t > 0, under some simple restrictions on the functional coefficient a(t), where (i)(0)O(t)(1+alpha)x is one of the fractional differential operators D-0(t)alpha(x'), ((0)D(t)(alpha)x)' = D-0(t)1+alpha x and D-0(t)alpha(tx' - x). Here, D-0(t)alpha designates the Riemann-Liouville derivative of order a E (0, 1). The asymptotic formula reads as [b + O(1)] . x(small) + c . x(large) as t -> +infinity for given b, c E is an element of R, where x(small) and x(large) represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation (i)(0)O(t)(1+alpha)x = 0, t > 0. (C) 2011 Elsevier Ltd. All rights reserved.
Citation Count: Baleanu, D...et al. (2011). Asymptotic integration of some nonlinear differential equations with fractional time derivative. Journal of Physics A-Mathematical and Theoretical, 44(5). http://dx.doi.org/ 10.1088/1751-8113/44/5/055203
Asymptotic integration of some nonlinear differential equations with fractional time derivative
(IOP Publishing Ltd, 2011) Baleanu, Dumitru; Agarwal, Ravi P.; Mustafa, Octavian G.; Cosulshci, Mirel
We establish that, under some simple integral conditions regarding the nonlinearity, the (1 + alpha)-order fractional differential equation (0)D(t)(alpha) (x') + f (t, x) = 0, t > 0, has a solution x is an element of C([0, +infinity), R) boolean AND C(1)((0, +infinity), R), with lim(t SE arrow 0) [t(1-alpha)x'(t)] is an element of R, which can be expanded asymptotically as a+bt(alpha)+O(t(alpha-1)) when t ->+infinity for given real numbers a, b. Our arguments are based on fixed point theory. Here, (0)D(t)(alpha) designates the Riemann-Liouville derivative of order alpha is an element of (0, 1)
Citation Count: Baleanu, D., Mustafa, O.G., Agarwal, R.P. (2010). Asymptotically linear solutions for some linear fractional differential equations. Abstract and Applied Analysis. http://dx.doi.org/ 10.1155/2010/865139
Asymptotically linear solutions for some linear fractional differential equations
(Hindawi Publishing Corporation, 2010) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.
We establish here that under some simple restrictions on the functional coefficient a(t) the fractional differential equation 0D(t)(alpha)[tx' - x + x(0)] + a(t)x = 0, t > 0, has a solution expressible as ct + d + o(1) for t -> +infinity, where D-0(t)alpha designates the Riemann-Liouville derivative of order alpha is an element of (0, 1) and c, d is an element of R
Citation Count: Baleanu, D.; Agarwal, P.; Purohit, S. D. "Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions", Scientific World Journal, (2013)
Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions
(Hindawi LTD, 2013) Baleanu, Dumitru; Agarwal, Ravi P.; Purohit, S. D.; 56389
We apply generalized operators of fractional integration involving Appell's function F-3(.) due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdelyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.
Citation Count: Jain, Shilpi...et al. (2019). "Certain Hermite-Hadamard Inequalities for Logarithmically Convex Functions with Applications", Mathematics, Vol. 7, No. 2.
Certain Hermite-Hadamard Inequalities for Logarithmically Convex Functions with Applications
(MDPI, 2019) Jain, Shilpi; Mehrez, Khaled; Baleanu, Dumitru; Agarwal, Ravi P.; 56389
In this paper, we discuss various estimates to the right-hand (resp. left-hand) side of the Hermite-Hadamard inequality for functions whose absolute values of the second (resp. first) derivatives to positive real powers are log-convex. As an application, we derive certain inequalities involving the q-digamma and q-polygamma functions, respectively. As a consequence, new inequalities for the q-analogue of the harmonic numbers in terms of the q-polygamma functions are derived. Moreover, several inequalities for special means are also considered.
Citation Count: Baleanu, Dimitru; Agarwal, Praveen, "Certain Inequalities Involving the Fractional q-Integral Operators", Abstract and Applied Analysis, (2014).
Certain Inequalities Involving the Fractional q-Integral Operators
(Hindawi LTD, 2014) Baleanu, Dumitru; Agarwal, Ravi P.; 56389
We establish some inequalities involving Saigo fractional q-integral operator in the theory of quantum calculus by using the two parameters of deformation, q(1) and q(2), whose special cases are shown to yield corresponding inequalities associated with Riemann-Liouville and Kober fractional q-integral operators, respectively. Furthermore, we also consider their relevance with other related known results.
Citation Count: Wang, G., Agarwal, P., Baleanu, D. (2015). Certain new gruss type inequalities involving saigo fractional q-integral operator. Journal of Computational Analysis and Application, 19(5), 862-873.
Certain new gruss type inequalities involving saigo fractional q-integral operator
(Eudoxus Press, 2015) Wang, Guotao; Agarwal, Ravi P.; Baleanu, Dumitru
In the present paper, we aim to investigate a new q-integral inequality of Gruss type for the Saigo fractional q-integral operator. Some special cases of our main results are also provided. The results presented in this paper improve and extend some recent results
Citation Count: Agarwal, Ravi P.; Karapınar, Erdal; Khojasteh, Farshid. (2022). "Cirić And Meir-Keeler Fixed Point Results In Super Metric Spaces", Applied Set-Valued Analysis and Optimization, Vol.4, No.3, pp.271-275.
Cirić And Meir-Keeler Fixed Point Results In Super Metric Spaces
(2022) Agarwal, Ravi P.; Karapınar, Erdal; Khojasteh, Farshid; 19184
In this paper, we consider Meir Keeler and Ćirić contractions in the setting of super metric spaces which is an interesting generalization of standard metric space. We investigate the existence and uniqueness of fixed points for these operators in this new structure.
Citation Count: Nyamoradi, Nemat; Baleanu, Dumitru; Agarwal, Ravi P. (2013). "Existence and uniqueness of positive solutions to fractional boundary value problems with nonlinear boundary conditions", Advances in Difference Equations.
Existence and uniqueness of positive solutions to fractional boundary value problems with nonlinear boundary conditions
(2013) Nyamoradi, Nemat; Baleanu, Dumitru; Agarwal, Ravi P.; 56389
In this manuscript, we consider two problems of boundary value problems for a fractional differential equation. A fixed point theorem in partially ordered sets and a contraction mapping principle are applied to prove the existence of at least one positive solution for both fractional boundary value problems.
Citation Count: Panda, Sumati Kumar; Agarwal, Ravi P.; Karapınar, Erdal. (2023). "Extended suprametric spaces and Stone-type theorem", AIMS Mathematics, Vol.8, No.10, pp.23183-23190.
Extended suprametric spaces and Stone-type theorem
(2023) Panda, Sumati Kumari; Agarwal, Ravi P.; Karapınar, Erdal; 19184
Extended suprametric spaces are defined, and the contraction principle is established using elementary properties of the greatest lower bound instead of the usual iteration procedure. Thereafter, some topological results and the Stone-type theorem are derived in terms of suprametric spaces. Also, we have shown that every suprametric space is metrizable. Further, we prove the existence of a solution of Ito-Doob type stochastic integral equations using our main fixed point theorem in extended suprametric spaces.
Citation Count: Baleanu, Dumitru...et al. (2017). Extension of the fractional derivative operator of the Riemann-Liouville, Journal of Nonlinear Sciences And Applications, 10(6), 2914-2924.
Extension of the fractional derivative operator of the Riemann-Liouville
(Int Scientific Research Publications, 2017) Baleanu, Dumitru; Agarwal, Ravi P.; Parmar, Rakesh K.; Alqurashi, Maysaa; Salahshour, Soheil; 56389
By using the generalized beta function, we extend the fractional derivative operator of the Riemann-Liouville and discusses its properties. Moreover, we establish some relations to extended special functions of two and three variables via generating functions. (C) 2017 All rights reserved.
Citation Count: Agarwal, Ravi P...et al. (2020). "F-contraction mappings on metric-like spaces in connection with integral equations on time scales", Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, Vol. 114, No. 3.
F-contraction mappings on metric-like spaces in connection with integral equations on time scales
(2020) Agarwal, Ravi P.; Aksoy, Ümit; Karapınar, Erdal; Erhan, İnci M.; 19184
In this paper we investigate the existence and uniqueness of fixed points of certain (ϕ, F) -type contractions in the frame of metric-like spaces. As an application of the theorem we consider the existence and uniqueness of solutions of nonlinear Fredholm integral equations of the second kind on time scales. We also present a particular example which demonstrates our theoretical results. © 2020, The Royal Academy of Sciences, Madrid.