Browsing by Author "Agarwal, Ravi P."
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Article Citation - WoS: 66Citation - Scopus: 72On Lp-solutions for a Class of Sequential Fractional Differential Equations(Elsevier Science inc, 2011) Mustafa, Octavian G.; Agarwal, Ravi P.; Baleanu, DumitruUnder some simple conditions on the coefficient a( t), we establish that the initial value problem ((0)D(t)(alpha)x)' + a(t)x = 0; t > 0; lim(t SE arrow 0)[t(1-alpha)x(t)] = 0 has no solution in L-p((1, +infinity), R), where p-1/p > alpha > 1/p and D-0(t)alpha designates the Riemann-Liouville derivative of order alpha Our result might be useful for developing a non-integer variant of H. Weyl's limit-circle/limit-point classification of differential equations. (C) 2011 Elsevier Inc. All rights reserved.Book Fixed Point Theory in Generalized Metric Spaces(2022) Karapınar, Erdal; Agarwal, Ravi P.This book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solve distinct real-world problems in computer science, engineering, and physics. The authors begin with an overview of the extension of metric spaces. Readers are introduced to general fixed-point theorems while comparing and contrasting important and insignificant metric spaces. The book is intended to be self-contained and serves as a unique resource for researchers in various disciplines.Article 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.Article Citation - WoS: 7Citation - Scopus: 12Fractional Hybrid Differential Equations and Coupled Fixed-Point Results for Α-Admissible F(Ψ1, Ψ2)-Contractions in M-Metric Spaces(Hindawi Ltd, 2020) Karapinar, Erdal; Moustafa, Shimaa, I; Shehata, Ayman; Agarwal, Ravi P.In this paper, we investigate the existence of a unique coupled fixed point for alpha-admissible mapping which is of F(psi(1),psi(2))-contraction in the context ofM-metric space. We have also shown that the results presented in this paper would extend many recent results appearing in the literature. Furthermore, we apply our results to develop sufficient conditions for the existence and uniqueness of a solution for a coupled system of fractional hybrid differential equations with linear perturbations of second type and with three-point boundary conditions.Article Oscillation criteria for even order dynamic equations on time-scales(2011) Grace, Said R.; Agarwal, Ravi P.; Kaymakçalan, BillurSome new criteria for the oscillation of even order linear dynamic equations on time-scales of the form xΔn(t) + q(t)x(t) = 0 are established.Article 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. (C) 2011 Elsevier Ltd. All rights reserved.Article Citation - WoS: 16Citation - Scopus: 18On a Multipoint Boundary Value Problem for a Fractional Order Differential Inclusion on an Infinite Interval(Hindawi Ltd, 2013) Baleanu, Dumitru; Agarwal, Ravi P.; Nyamoradi, NematWe investigate the existence of solutions for the following multipoint boundary value problem of a fractional order differential inclusion D(0+)(alpha)u(t) + F(t,u(t),u'(t)) (sic) 0, 0 < t < +infinity,u(0) = u'(0) = 0, D(alpha-1)u(+infinity) - Sigma(m-2)(i-1) beta(i)u(xi(i)) = 0, where D-0+(alpha) is the standard Riemann-Liouville fractional derivative, 2 < alpha < 3, 0 < xi(1) < xi(2) < center dot center dot center dot < xi(m-2) < +infinity, satisfies 0 < Sigma(m-2)(i=1) beta(i)xi(alpha-1)(i) < Gamma(alpha), and F : [0, +infinity) x R x R (sic) P(R) is a set-valued map. Several results are obtained by using suitable fixed point theorems when the right hand side has convex or nonconvex values.Article Citation - WoS: 46Citation - Scopus: 58Nonlocal Nonlinear Integrodifferential Equations of Fractional Orders(Springer, 2012) Baleanu, Dumitru; Agarwal, Ravi P.; Debbouche, AmarIn this paper, Schauder fixed point theorem, Gelfand-Shilov principles combined with semigroup theory are used to prove the existence of mild and strong solutions for nonlinear fractional integrodifferential equations of Sobolev type with nonlocal conditions in Banach spaces. To illustrate our abstract results, an example is given. MSC: 35A05, 34G20, 34K05, 26A33.Article Citation - WoS: 66Citation - Scopus: 73Two Fractional Derivative Inclusion Problems Via Integral Boundary Condition(Elsevier Science inc, 2015) Baleanu, Dumitru; Hedayati, Vahid; Rezapour, Shahram; Agarwal, Ravi P.The goal of the manuscript is to analyze the existence of solutions for the Caputo fractional differential inclusion (c)D(q)x(t) is an element of F(t,x(t), (c)D(beta)x(t)) with the boundary value conditions x(0) = 0 and x(1) + x'(1) = integral(eta)(0) x(s)ds, such that 0 < eta < 1, 1 < q <= 2, 0 < beta < 1 and q = beta > 1. Also, we investigate the existence of solutions for the Caputo fractional differential inclusion (c)D(q)x(t) is an element of F(t,x(t)) such that x(0) = a integral(nu)(0) x(s)ds and x(1) = b integral(eta)(0) x(s)ds, where 0 < nu, eta < 1, 1 < q <= 2 and a, b is an element of R. (C) 2014 Elsevier Inc. All rights reserved.Article FractionalHybridDifferential EquationsandCoupled Fixed-Point Results for α-Admissible F(ψ1, ψ2) − Contractions in M − Metric Spaces(2020) Karapınar, Erdal; Shimaa I., Moustafa; Shehata, Ayman; Agarwal, Ravi P.In this paper, we investigate the existence of a unique coupled fixed point for admissible mapping which is of contraction in the context of metric space. We have also shown that the results presented in this paper would extend many recent results appearing in the literature. Furthermore, we apply our results to develop sufficient conditions for the existence and uniqueness of a solution for a coupled system of fractional hybrid differential equations with linear perturbations of second type and with three-point boundary conditions.Article Citation - WoS: 15Citation - Scopus: 28Asymptotically Linear Solutions for Some Linear Fractional Differential Equations(Hindawi Publishing Corporation, 2010) Mustafa, Octavian G.; Agarwal, Ravi P.; Baleanu, DumitruWe 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.Article Citation - WoS: 60Citation - Scopus: 72A Survey:f-Contractions With Related Fixed Point Results(Springer Basel Ag, 2020) Fulga, Andreea; Agarwal, Ravi P.; Karapinar, ErdalIn 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.Article Citation - WoS: 9Citation - Scopus: 9The Existence and Uniqueness of Solutions for a Class of Nonlinear Fractional Differential Equations With Infinite Delay(Hindawi Ltd, 2013) Baleanu, Dumitru; Agarwal, Ravi P.; Babakhani, AzizollahWe prove the existence and uniqueness of solutions for two classes of infinite delay nonlinear fractional order differential equations involving Riemann-Liouville fractional derivatives. The analysis is based on the alternative of the Leray-Schauder fixed-point theorem, the Banach fixed-point theorem, and the Arzela-Ascoli theorem in Omega = {y : (-infinity,b] -> R : y vertical bar(<-infinity, 0]) epsilon B} such that y vertical bar ([0,b]) is continuous and B is a phase space.Article Asymptotic Integration of (1 + Α) -Order Fractional Differential Equations(2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.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>0Article Citation - WoS: 78Citation - Scopus: 88On the Solution Set for a Class of Sequential Fractional Differential Equations(Iop Publishing Ltd, 2010) Mustafa, Octavian G.; Agarwal, Ravi P.; Baleanu, DumitruWe establish here that under some simple restrictions on the functional coefficient a(t) the solution set of the fractional differential equation ((0)D(t)(alpha)x)' + a(t) x = 0 splits between eventually small and eventually large solutions as t -> +infinity, where D-0(t)alpha designates the Riemann-Liouville derivative of the order alpha is an element of (0, 1).Article Citation - WoS: 9Citation - Scopus: 10Identifying the Source Function for Time Fractional Diffusion With Non-Local in Time Conditions(Springer Heidelberg, 2021) Baleanu, Dumitru; Agarwal, Ravi P.; Long, Le Dinh; Luc, Nguyen HoangThe diffusion equation has many applications in fields such as physics, environment, and fluid mechanics. In this paper, we consider the problem of identifying an unknown source for a time-fractional diffusion equation in a general bounded domain from the nonlocal integral condition. The problem is non-well-posed in the sense of Hadamard, i.e, if the problem has only one solution, the solution will not depend continuously on the input data. To get a stable solution and approximation, we need to offer the regularization methods. The first contribution to the paper is to provide a regularized solution using the modified fractional Landweber method. Two choices are proposed including a priori and a posteriori parameter choice rules, to estimate the convergence rate of the regularized methods. The second new contribution is to use truncation to give an estimate of L-p for the convergence rate.Article Citation - WoS: 20Citation - Scopus: 28On the Existence of Solution for Fractional Differential Equations of Order 3 < Δ1 ≤ 4(Springer, 2015) Agarwal, Ravi P.; Khan, Rahmat Ali; Jafari, Hossein; Baleanu, Dumitru; Khan, HasibIn this paper, we deal with a fractional differential equation of order delta(1) is an element of (3,4] with initial and boundary conditions, D-delta 1 psi(x) = -H(x,psi(x)), D-alpha 1 psi(1) = 0 = I3-delta 1 psi(0) = I4-delta 1 psi(0), psi(1) = Gamma(delta(1)-alpha(1))/Gamma(nu(1)) I delta 1-alpha 1 H(x,psi(x))(1), where x is an element of [0, 1], alpha(1) is an element of (1, 2], addressing the existence of a positive solution (EPS), where the fractional derivatives D-delta 1, D-alpha 1 are in the Riemann-Liouville sense of the order delta(1), alpha(1), respectively. The function H is an element of C([0, 1] x R, R) and I delta 1-alpha 1 H(x, psi(x))(1) = 1/Gamma(delta(1)-alpha(1)) integral(1)(0) (1 -z)(delta 1-alpha 1-1) H(z,psi(z)) dz. To this aim, we establish an equivalent integral form of the problem with the help of a Green's function. We also investigate the properties of the Green's function in the paper which we utilize in our main result for the EPS of the problem. Results for the existence of solutions are obtained with the help of some classical results.Article Citation - WoS: 164Citation - Scopus: 177A Survey on Fuzzy Fractional Differential and Optimal Control Nonlocal Evolution Equations(Elsevier, 2018) Baleanu, Dumitru; Nieto, Juan J.; Torres, Delfim F. M.; Zhou, Yong; Agarwal, Ravi P.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.Article Citation - WoS: 28Citation - Scopus: 30Asymptotic Integration of (1+α)-Order Fractional Differential Equations(Pergamon-elsevier Science Ltd, 2011) Mustafa, Octavian G.; Agarwal, Ravi P.; Baleanu, DumitruWe 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.Article Citation - WoS: 78Citation - Scopus: 97Some Existence Results for a Nonlinear Fractional Differential Equation on Partially Ordered Banach Spaces(Springeropen, 2013) Agarwal, Ravi P.; Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, DumitruBy using fixed point results on cones, we study the existence and uniqueness of positive solutions for some nonlinear fractional differential equations via given boundary value problems. Examples are presented in order to illustrate the obtained results.
