Research Article
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Year 2022, Volume 5, Issue 3, 114 - 123, 30.09.2022
https://doi.org/10.33434/cams.1069182

Abstract

References

  • [1] D. R. Anderson, D. J. Ulness, Properties of Katugampola fractional derivative with potential application in quantum mechanics, J. Math. Phys., 56 (2015).
  • [2] M. S. Abdo, Further results on the existence of solutions for generalized fractional quadratic functional integral equations, J. Math. Anal & Model, 1(1) (2020), 33-46.
  • [3] A. Bashir, S. Sivasundaram, Some existence results for fractional integro-differential equations with nonlinear conditions, Comm. Appl. Analysis, 12 (2) (2008), 107-112.
  • [4] B. N. Abood, S. S. Redhwan, O. Bazighifan, K. Nonlaopon, Investigating a generalized fractional quadratic integral equation, Fractal Fract., 6 (2022), 251.
  • [5] M. Benchohra, K. Maazouz, Existence and uniqueness results for implicit fractional differential equations with integral boundary conditions, Comm. App. Analysis, 20 (2016), 355-366.
  • [6] A. Cabada, K. Maazouz, Results for Fractional Differential Equations with Integral Boundary Conditions Involving the Hadamard Derivative, In: Area I. et al. (eds) Nonlinear Analysis and Boundary Value Problems, NABVP 2018, Springer Proceedings in Mathematics & Statistics, vol 292. Springer, Cham, 2019.
  • [7] G. J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003.
  • [8] M. Janaki, K. Kanagarajan, E. M. Elsayed, Existence criteria for Katugampola fractional type impulsive differential equations with inclusions, J. Math. Sci. Model., 2(1) (2019), 51-63.
  • [9] M. Janaki, K. Kanagarajan, D. Vivek, Analytic study on fractional implicit differential equations with impulses via Katugampola fractional Derivative, Int. J. Math. Appl., 6(2-A) (2018), 53-62.
  • [10] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
  • [11] U. N. Katugampola, New approach to generalized fractional integral, Appl. Math. Comput., 218(3) (2011), 860-865.
  • [12] U. N Katugampola, New approach to generalized fractional derivative, Bull. Math. Anal. Appl., 6 (4) (2014), 1-15.
  • [13] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differenatial Equations, North-Holland Mathematics Studies, 204, Elsevier Science B. V. Amsterdam, 2006.
  • [14] V. Lakshmikantham, S. Leela, J. Vasundhara, Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, 2009.
  • [15] F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity. An Introduction to Mathematical Models, Imperial College Press, London, 2010.
  • [16] K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993. [17] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [18] S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Yverdon, 1993.
  • [19] D. R. Smart, Fixed Point Theorems, Cambridge University Press, Cambridge 1974, Bull. Math. Anal. Appl., 6 (4) (2014), 1-15.
  • [20] S. S. Redhwan, S. L. Shaikh, M. S. Abdo, Caputo-Katugamola type implicit fractional differential equation with two-point anti-periodic boundary conditions, Results in Nonlinear Analysis, 5(1) (2022), 12-28.
  • [21] S. S. Redhwan, S. L. Shaikh, M. S. Abdo, W. Shatanawi, K. Abodayeh, M. A. Almalahi, T. Aljaaidi, Investigating a generalized Hilfer-type fractional differential equation with two-point and integral boundary conditions, AIMS Math., 7(2) (2021), 1856-187.
  • [22] D. Vivek, E. M. Elsayed, K. Kanagarajan, Dynamics and stability results for impulsive type integro-differential equations with generalized fractional derivative, Math. Nat. Sci., 4 (2019), 1-12.
  • [23] D. Vivek, K. Kanagarajan, S. Harikrishnan, Theory and analysis of impulsive type pantograph equations with Katugampola fractioanl derivative, J. Vabration Testing and System Dynamic, 2 (1) 2018, 9-20.
  • [24] D. Vivek, E. M. Elsayed, K. Kanagarajan, Theory of fractional implicit differential equations with complex order, J. Uni. Math., 2(2) (2019), 154-165.
  • [25] H. Wang, Existence results for fractional functional differential equations with impulses, J. Appl. Math. Comput., 38 (2012), 85-101.
  • [26] E. Zeidler, Nonlinear functional Analysis and its Applications-I Fixed Point Theorem, Springer, New-York, 1993.

Existence Results for BVP of a Class of Generalized Fractional-Order Implicit Differential Equations

Year 2022, Volume 5, Issue 3, 114 - 123, 30.09.2022
https://doi.org/10.33434/cams.1069182

Abstract

In this paper, we study the existence of solutions to boundary value problem for implicit differential equations involving generalized fractional derivative via fixed point methods.

References

  • [1] D. R. Anderson, D. J. Ulness, Properties of Katugampola fractional derivative with potential application in quantum mechanics, J. Math. Phys., 56 (2015).
  • [2] M. S. Abdo, Further results on the existence of solutions for generalized fractional quadratic functional integral equations, J. Math. Anal & Model, 1(1) (2020), 33-46.
  • [3] A. Bashir, S. Sivasundaram, Some existence results for fractional integro-differential equations with nonlinear conditions, Comm. Appl. Analysis, 12 (2) (2008), 107-112.
  • [4] B. N. Abood, S. S. Redhwan, O. Bazighifan, K. Nonlaopon, Investigating a generalized fractional quadratic integral equation, Fractal Fract., 6 (2022), 251.
  • [5] M. Benchohra, K. Maazouz, Existence and uniqueness results for implicit fractional differential equations with integral boundary conditions, Comm. App. Analysis, 20 (2016), 355-366.
  • [6] A. Cabada, K. Maazouz, Results for Fractional Differential Equations with Integral Boundary Conditions Involving the Hadamard Derivative, In: Area I. et al. (eds) Nonlinear Analysis and Boundary Value Problems, NABVP 2018, Springer Proceedings in Mathematics & Statistics, vol 292. Springer, Cham, 2019.
  • [7] G. J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003.
  • [8] M. Janaki, K. Kanagarajan, E. M. Elsayed, Existence criteria for Katugampola fractional type impulsive differential equations with inclusions, J. Math. Sci. Model., 2(1) (2019), 51-63.
  • [9] M. Janaki, K. Kanagarajan, D. Vivek, Analytic study on fractional implicit differential equations with impulses via Katugampola fractional Derivative, Int. J. Math. Appl., 6(2-A) (2018), 53-62.
  • [10] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
  • [11] U. N. Katugampola, New approach to generalized fractional integral, Appl. Math. Comput., 218(3) (2011), 860-865.
  • [12] U. N Katugampola, New approach to generalized fractional derivative, Bull. Math. Anal. Appl., 6 (4) (2014), 1-15.
  • [13] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differenatial Equations, North-Holland Mathematics Studies, 204, Elsevier Science B. V. Amsterdam, 2006.
  • [14] V. Lakshmikantham, S. Leela, J. Vasundhara, Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, 2009.
  • [15] F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity. An Introduction to Mathematical Models, Imperial College Press, London, 2010.
  • [16] K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993. [17] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [18] S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Yverdon, 1993.
  • [19] D. R. Smart, Fixed Point Theorems, Cambridge University Press, Cambridge 1974, Bull. Math. Anal. Appl., 6 (4) (2014), 1-15.
  • [20] S. S. Redhwan, S. L. Shaikh, M. S. Abdo, Caputo-Katugamola type implicit fractional differential equation with two-point anti-periodic boundary conditions, Results in Nonlinear Analysis, 5(1) (2022), 12-28.
  • [21] S. S. Redhwan, S. L. Shaikh, M. S. Abdo, W. Shatanawi, K. Abodayeh, M. A. Almalahi, T. Aljaaidi, Investigating a generalized Hilfer-type fractional differential equation with two-point and integral boundary conditions, AIMS Math., 7(2) (2021), 1856-187.
  • [22] D. Vivek, E. M. Elsayed, K. Kanagarajan, Dynamics and stability results for impulsive type integro-differential equations with generalized fractional derivative, Math. Nat. Sci., 4 (2019), 1-12.
  • [23] D. Vivek, K. Kanagarajan, S. Harikrishnan, Theory and analysis of impulsive type pantograph equations with Katugampola fractioanl derivative, J. Vabration Testing and System Dynamic, 2 (1) 2018, 9-20.
  • [24] D. Vivek, E. M. Elsayed, K. Kanagarajan, Theory of fractional implicit differential equations with complex order, J. Uni. Math., 2(2) (2019), 154-165.
  • [25] H. Wang, Existence results for fractional functional differential equations with impulses, J. Appl. Math. Comput., 38 (2012), 85-101.
  • [26] E. Zeidler, Nonlinear functional Analysis and its Applications-I Fixed Point Theorem, Springer, New-York, 1993.

Details

Primary Language English
Subjects Mathematics
Journal Section Articles
Authors

Kadda MAAZOUZ>
It is not affiliated with an institution
0000-0003-2237-2713
Türkiye


Dvivek VİVEK>
It is not affiliated with an institution
0000-0003-0951-8060
Türkiye


Elsayed ELSAYED> (Primary Author)
King Abdulaziz University
0000-0003-0894-8472
Saudi Arabia

Supporting Institution -
Project Number -
Publication Date September 30, 2022
Submission Date February 7, 2022
Acceptance Date September 12, 2022
Published in Issue Year 2022, Volume 5, Issue 3

Cite

Bibtex @research article { cams1069182, journal = {Communications in Advanced Mathematical Sciences}, issn = {2651-4001}, address = {}, publisher = {Emrah Evren KARA}, year = {2022}, volume = {5}, number = {3}, pages = {114 - 123}, doi = {10.33434/cams.1069182}, title = {Existence Results for BVP of a Class of Generalized Fractional-Order Implicit Differential Equations}, key = {cite}, author = {Maazouz, Kadda and Vivek, Dvivek and Elsayed, Elsayed} }
APA Maazouz, K. , Vivek, D. & Elsayed, E. (2022). Existence Results for BVP of a Class of Generalized Fractional-Order Implicit Differential Equations . Communications in Advanced Mathematical Sciences , 5 (3) , 114-123 . DOI: 10.33434/cams.1069182
MLA Maazouz, K. , Vivek, D. , Elsayed, E. "Existence Results for BVP of a Class of Generalized Fractional-Order Implicit Differential Equations" . Communications in Advanced Mathematical Sciences 5 (2022 ): 114-123 <https://dergipark.org.tr/en/pub/cams/issue/72815/1069182>
Chicago Maazouz, K. , Vivek, D. , Elsayed, E. "Existence Results for BVP of a Class of Generalized Fractional-Order Implicit Differential Equations". Communications in Advanced Mathematical Sciences 5 (2022 ): 114-123
RIS TY - JOUR T1 - Existence Results for BVP of a Class of Generalized Fractional-Order Implicit Differential Equations AU - KaddaMaazouz, DvivekVivek, ElsayedElsayed Y1 - 2022 PY - 2022 N1 - doi: 10.33434/cams.1069182 DO - 10.33434/cams.1069182 T2 - Communications in Advanced Mathematical Sciences JF - Journal JO - JOR SP - 114 EP - 123 VL - 5 IS - 3 SN - 2651-4001- M3 - doi: 10.33434/cams.1069182 UR - https://doi.org/10.33434/cams.1069182 Y2 - 2022 ER -
EndNote %0 Communications in Advanced Mathematical Sciences Existence Results for BVP of a Class of Generalized Fractional-Order Implicit Differential Equations %A Kadda Maazouz , Dvivek Vivek , Elsayed Elsayed %T Existence Results for BVP of a Class of Generalized Fractional-Order Implicit Differential Equations %D 2022 %J Communications in Advanced Mathematical Sciences %P 2651-4001- %V 5 %N 3 %R doi: 10.33434/cams.1069182 %U 10.33434/cams.1069182
ISNAD Maazouz, Kadda , Vivek, Dvivek , Elsayed, Elsayed . "Existence Results for BVP of a Class of Generalized Fractional-Order Implicit Differential Equations". Communications in Advanced Mathematical Sciences 5 / 3 (September 2022): 114-123 . https://doi.org/10.33434/cams.1069182
AMA Maazouz K. , Vivek D. , Elsayed E. Existence Results for BVP of a Class of Generalized Fractional-Order Implicit Differential Equations. Communications in Advanced Mathematical Sciences. 2022; 5(3): 114-123.
Vancouver Maazouz K. , Vivek D. , Elsayed E. Existence Results for BVP of a Class of Generalized Fractional-Order Implicit Differential Equations. Communications in Advanced Mathematical Sciences. 2022; 5(3): 114-123.
IEEE K. Maazouz , D. Vivek and E. Elsayed , "Existence Results for BVP of a Class of Generalized Fractional-Order Implicit Differential Equations", Communications in Advanced Mathematical Sciences, vol. 5, no. 3, pp. 114-123, Sep. 2022, doi:10.33434/cams.1069182
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