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APPROXIMATE ENDPOINT SOLUTIONS FOR A CLASS OF FRACTIONAL $q$ $q$ -DIFFERENTIAL INCLUSIONS BY COMPUTATIONAL RESULTS

Department of Mathematics, Istanbul Technical University, Istanbul, Turkey

CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México

E-mail Address: jose.ga@cenidet.tecnm.mx

Corresponding authors.

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D. BALEANU

Department of Mathematics, Cankaya University, Ogretmenler Cad. 14 06530, Balgat, Ankara, Turkey

Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

Institute of Space Sciences, Magurele, Bucharest, Romania

E-mail Address: aumitru.baleanu@gmail.com

Corresponding authors.

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SH. REZAPOUR

Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

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, and

M. E. SAMEI

Department of Mathematics, Faculty of Basic Science, Bu-Ali Sina University, Hamedan 65178, Iran

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https://doi.org/10.1142/S0218348X20400290Cited by:19 (Source: Crossref)

This article is part of the issue:

Special Issue on Fractal and Fractional with Applications to Nature
Guest Editors: Abdon Atangana, Emile Franc Goufo Ndongmo, José Francisco Gómez Aguilar, Muhammad Altaf Khan and Ilknur Koca

Abstract

By using the notion of endpoints for set-valued functions and some classical fixed point techniques, we investigate the existence of solutions for two fractional $q$ $q$ -differential inclusions under some integral boundary value conditions. By providing an example, we illustrate our main result about endpoint. Also, we give some related algorithms and numerical results.

Keywords:

References

1. F. H. Jackson, $q$ $q$ -difference equations, Am. J. Math. 32 (1910) 305–314. Crossref, Google Scholar
2. C. R. Adams, The general theory of a class of linear partial $q$ $q$ -difference equations, Trans. Amer. Math. Soc. 26(2) (1924) 283–312. Google Scholar
3. C. R. Adams, Note on the integro- $q$ $q$ -difference equations, Trans. Amer. Math. Soc. 31(4) (1929) 861–867. Google Scholar
4. B. Ahmad, S. Etemad, M. Ettefagh and Sh. Rezapour, On the existence of solutions for fractional $q$ $q$ -difference inclusions with $q$ $q$ -antiperiodic boundary conditions, Bull. Math. Soc. Sci. Math. Roumanie 59(2)(107) (2016) 119–134. Google Scholar
5. B. Ahmad, J. J. Nieto, A. Alsaedi and H. Al-Hutami, Existence of solutions for nonlinear fractional $q$ $q$ -difference integral equations with two fractional orders and nonlocal four-point boundary conditions, J. Franklin Inst. 351 (2014) 2890–2909. Crossref, Web of Science, Google Scholar
6. B. Ahmad, S. K. Ntouyas and I. K. Purnaras, Existence results for nonlocal boundary value problems of nonlinear fractional $q$ $q$ -difference equations, Adv. Diff. Equ. 2012 (2012) 140. Crossref, Web of Science, Google Scholar
7. N. Balkani, Sh. Rezapour and R. H. Haghi, Approximate solutions for a fractional $q$ $q$ -integro-difference equation, J. Math. Extension 13(3) (2019) 109–119. Web of Science, Google Scholar
8. R. A. C. Ferreira, Nontrivials solutions for fractional $q$ $q$ -difference boundary value problems, Elect. J. Qual. Theory Diff. Equ. 70 (2010) 1–101. Google Scholar
9. V. Kalvandi and M. E. Samei, New stability results for a sum-type fractional $q$ $q$ -integro-differential equation, J. Adv. Math. Stud. 12(2) (2019) 201–209. Google Scholar
10. S. K. Ntouyas and M. E. Samei, Existence and uniqueness of solutions for multi-term fractional $q$ $q$ -integro-differential equations via quantum calculus, Adv. Diff. Equ. 2019 (2019) 475. https://doi.org/10.1186/s13662-019-2414-8 Crossref, Web of Science, Google Scholar
11. M. E. Samei, Gh. Khalilzadeh Ranjbar and V. Hedayati, Existence of solutions for equations and inclusions of multi-term fractional $q$ $q$ -integro-differential with non-separated and initial boundary conditions, J. Ineq. Appl. 2019 (2019) 273. Crossref, Web of Science, Google Scholar
12. M. E. Samei and G. Khalilzadeh Ranjbar, Some theorems of existence of solutions for fractional hybrid $q$ $q$ -difference inclusion, J. Adv. Math. Stud. 12(1) (2019) 63–76. Google Scholar
13. Y. Zhao, H. Chen and Q. Zhang, Existence results for fractional $q$ $q$ -difference equations with nonlocal $q$ $q$ -integral boundary conditions, Adv. Diff. Equ. 2013 (2013) 48. Crossref, Web of Science, Google Scholar
14. R. P. Agarwal, D. Baleanu, V. Hedayati and Sh. Rezapour, Two fractional derivative inclusion problems via integral boundary condition, Appl. Math. Comput. 257 (2015) 205–212. Web of Science, Google Scholar
15. N. Aghazadeh, E. Ravash and Sh. Rezapour, Existence results and numerical solutions for a multi-term fractional integro-differential equation, Kragujevac J. Math. 43(3) (2019) 413–426. Web of Science, Google Scholar
16. E. Akbari Kojabad and Sh. Rezapour, Approximate solutions of a sum-type fractional integro-differential equation by using Chebyshev and Legendre polynomials, Adv. Diff. Equ. 2017 (2017) 351. Crossref, Web of Science, Google Scholar
17. D. Baleanu, V. Hedayati, Sh. Rezapour and M. M. Al-Qurashi, On two fractional differential inclusions, Springerplus 5(1) (2016) 882. Crossref, Google Scholar
18. D. Baleanu, Sh. Rezapour and Z. Saberpour, On fractional integro-differential inclusions via the extended fractional Caputo–Fabrizio derivation, Bound. Value Probl. 2019 (2019) 79. Crossref, Web of Science, Google Scholar
19. M. De La Sena, V. Hedayati, Y. Gholizade Atani and Sh. Rezapour, The existence and numerical solution for a $k$ $k$ -dimensional system of multi-term fractional integro-differential equations, Nonlinear Anal. Model. Control 22(2) (2017) 188–209. Crossref, Web of Science, Google Scholar
20. V. Hedayati and M. E. Samei, Positive solutions of fractional differential equation with two pieces in chain interval and simultaneous dirichlet boundary conditions, Bound. Val. Probl. 2019 (2019) 141. https://doi.org/10.1186/s13661-019-1251-8 Crossref, Web of Science, Google Scholar
21. A. Mohammadi, N. Aghazadeh and Sh. Rezapour, Haar wavelet collocation method for solving singular and nonlinear fractional time-dependent Emden–Fowler equations with initial and boundary conditions, Math. Sci. 13 (2019) 255–265. Crossref, Google Scholar
22. Sh. Rezapour and V. Hedayati, On a Caputo fractional differential inclusion with integral boundary condition for convex-compact and nonconvex-compact valued multifunctions, Kragujevac J. Math. 41(1) (2017) 143–158. Crossref, Web of Science, Google Scholar
23. M. E. Samei, V. Hedayati and Sh. Rezapour, Existence results for a fractional hybrid differential inclusion with Caputo-Hadamard type fractional derivative, Adv. Differ. Equ. 2019 (2019) 163. Crossref, Web of Science, Google Scholar
24. M. Shabibi, M. Postolache, Sh. Rezapour and S. M. Vaezpour, Investigation of a multi-singular pointwise defined fractional integro-differential equation, J. Math. Anal. 7(5) (2016) 61–77. Google Scholar
25. M. Shabibi, Sh. Rezapour and S. M. Vaezpour, A singular fractional integro-differential equation, Sci. Bull. Univ. Politeh. Buch. A 79(1) (2017) 109–118. Google Scholar
26. S. Liang and M. E. Samei, New approach to solutions of a class of singular fractional $q$ $q$ -differential problem via quantum calculus, Adv. Diff. Equ. 2019 (2019) 163. https://doi.org/10.1186/s13662-019-2489-2 Google Scholar
27. M. E. Samei, Existence of solutions for a system of singular sum fractional $q$ $q$ -differential equations via quantum calculus, Adv. Diff. Equ. 2019 (2019) 163. https://doi.org/10.1186/s13662-019-2480-y Crossref, Web of Science, Google Scholar
28. M. Kisielewicz, Differential Inclusions and Optimal Control (Kluwer, Dordrecht, 1991). Google Scholar
29. A. Amini-Harandi, Endpoints of set-valued contractions in metric spaces, Nonlinear Anal. 72 (2010) 132–134. Crossref, Web of Science, Google Scholar
30. M. E. Samei, V. Hedayati and G. K. Ranjbar, The existence of solution for $k$ $k$ -dimensional system of Langevin Hadamard-type fractional differential inclusions with $2 k$ $2 k$ different fractional orders, Mediterranean J. Math. 17 (2020) 37. https://doi.org/10.1007/s00009-019-1471-2 Crossref, Web of Science, Google Scholar

Vol. 28, No. 08

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History

Received 19 December 2019

Accepted 16 February 2020

Published: June 13, 2020

Information

This is an Open Access article in the “Special Issue on Fractal and Fractional with Applications to Nature” published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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APPROXIMATE ENDPOINT SOLUTIONS FOR A CLASS OF FRACTIONAL qq<math altimg="eq-00001.gif" display="inline"><mi>q</mi></math>-DIFFERENTIAL INCLUSIONS BY COMPUTATIONAL RESULTS

Abstract

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APPROXIMATE ENDPOINT SOLUTIONS FOR A CLASS OF FRACTIONAL $q$ $q$ -DIFFERENTIAL INCLUSIONS BY COMPUTATIONAL RESULTS