Generalized fractional delay functional equations with Riemann-Stieltjes and infinite point nonlocal conditions

Volume 24, Issue 1, pp 33--48 http://dx.doi.org/10.22436/jmcs.024.01.04

Publication Date: December 23, 2020 Submission Date: July 21, 2020 Revision Date: September 22, 2020 Accteptance Date: November 20, 2020

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1054 Downloads
• 2233 Views

Authors

M. I. Youssef - Department of Mathematics, College of Science, Jouf University, P. O. Box 2014, Sakaka, Saudi Arabia. - Department of Mathematics, Faculty of Education, Alexandria University, Alexandria , Egypt.

Abstract

In the current work, we investigate the solvability of a general class of fractional delay functional equations subject to an infinite point non-classical condition, and the Riemann-Stieltjes integral condition as well. First, the existence of solutions is investigated. Second, the continuous dependence of solution is studied in three different cases. Third, illustrative examples are given to support our results. Our work extends some developments published recently in that field.

Share and Cite

Keywords

• Fractional integro-differential equation
• existence of solutions
• infinite point non-classical condition
• Riemann-Stieltjes nonlocal condition
• delay function

MSC

•  34A12
•  45D05
•  34K37

References

• [1] R. P. Agarwal, M. Meehan, D. O'Regan, Fixed Point Theory and Applications, Cambridge University Press, Cambridge (2001)
  • View Article
  • MathSciNet
  • Google Scholar


• [2] R. Almeida, A. B. Malinowska, T. Odzijewicz, Fractional differential equations with dependence on the Caputo-Katugampola derivative, J. Comput. Nonlinear Dynam., 11 (2016), 11 pages
  • View Article
  • Google Scholar


• [3] A. T. Assanova, On the theory of nonlocal problems with integral conditions for systems of equations of hyperbolic type, Ukrainian Math. J., 70 (2019), 1514--1525
  • View Article
  • Google Scholar


• [4] T. M. Atanacković, S. Pilipović, B. Stanković, D. Zorica, Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion Processes, John Wiley & Sons, Hoboken (2014)
  • View Article
  • Google Scholar
  • MATH


• [5] G. Avalishvili, M. Avalishvili, D. Gordeziani, On a nonlocal problem with integral boundary conditions for a multidimensional elliptic equation, Appl. Math. Lett., 24 (2011), 566--571
  • View Article
  • MathSciNet
  • Google Scholar


• [6] R. Barretta, F. Marotti de Sciarra, Constitutive boundary conditions for nonlocal strain gradient elastic nano-beams, Internat. J. Engrg. Sci., 130 (2018), 187--198
  • View Article
  • MathSciNet
  • Google Scholar


• [7] A. Bellen, M. Zennaro, Numerical methods for delay differential equations, Oxford University Press, New York (2003)
  • View Article
  • MathSciNet
  • Google Scholar


• [8] V. Daftardar-Gejji, Fractional Calculus and Fractional Differential Equations, Birkhauser, Singapore (2019)
  • View Article
  • MATH


• [9] M. M. Elborai, M. I. Youssef, On stochastic solutions of nonlocal random functional integral equations, Arab J. Math. Sci., 25 (2019), 180--188
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] A. El-Sayed, R. Gamal, Infinite point and Riemann-Stieltjes integral conditions for an integro-differential equation, Nonlinear Anal. Model. Control, 24 (2019), 733--754
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [11] M. A. E. Herzallah, Notes on some fractional calculus operators and their properties, J. Fract. Calc. Appl., 5 (2014), 10 pages
  • View Article
  • MathSciNet
  • Google Scholar


• [12] U. N. Katugampola, New approach to a generalized fractional integral, Appl. Math. Comput., 218 (2011), 860--865
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [13] U. N. Katugampola, A new approach to generalized fractional derivatives, Bull. Math. Anal. Appl., 6 (2014), 1--15
  • View Article
  • Google Scholar


• [14] A. I. Kozhanov, Nonlocal problems with integral conditions for elliptic equations, Complex Var. Elliptic Equ., 64 (2019), 741--752
  • View Article
  • MathSciNet
  • Google Scholar


• [15] L. T. P. Ngoc, N. A. Triet, A. P. N. Dinh, N. T. Long, Existence and exponential decay of solutions for a wave equation with integral nonlocal boundary conditions of memory type, Numer. Funct. Anal. Optim., 38 (2017), 1173--1207
  • View Article
  • MathSciNet
  • Google Scholar


• [16] A. Ricardo, Variational Problems Involving a Caputo-Type Fractional Derivative, J. Optim. Theory Appl., 174 (2017), 276--294
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [17] H. G. Sun, Y. Zhang, D. Baleanu, W. Chen, Y. Q. Chen, A new collection of real world applications of fractional calculus in science and engineering, Commun. Nonlinear Sci. Numer. Simul., 64 (2018), 213--231
  • View Article
  • Google Scholar


• [18] K. Szymańska-Dębowska, On the existence of solutions for nonlocal boundary value problems, Georgian Math. J., 22 (2015), 273--279
  • View Article
  • MathSciNet
  • Google Scholar


• [19] M. I. Youssef, Caputo-Katugampola fractional Volterra functional differential equations with a vanishing lag function, J. Nonlinear Sci. Appl., 13 (2020), 293--302
  • View Article
  • MathSciNet
  • Google Scholar


• [20] M. I. Youssef, On the solvability of a general class of a coupled system of stochastic functional integral equations, Arab J. Basic Appl. Sci., 27 (2020), 142--148
  • View Article
  • Google Scholar