Existence and stability results for $\psi$-Caputo fractional integrodifferential equations with delay

Authors

  • Prabu D Ph.D

DOI:

https://doi.org/10.62918/hjma.v2i2.26

Keywords:

fractional differential equations, $\psi$-fractional derivative, fixed point

Abstract

This paper deals with the existence and uniqueness results for $\psi$-Caputo fractional integrodifferential equations with finite delay. The results are obtained by using the standard fixed point theorems. An example is given to show the main discoveries.

References

B. Abdellatif, S.A. Mohammed, and B. Maamar, Existence results for $psi$-Caputo fractional neutral functional integrodifferential equations with finite delay, Turkish Journal of Mathematics, 44 (2020), 2380--2401.

R. Almeida, A Caputo fractional derivative of a function with respect to another function, Communications in Nonlinear Science and Numerical Simulation, 44 (2017), 460--481.

R. Almeida, Functional differential equations involving the $psi$-Caputo fractional derivative, Fractal and Fractional, 4(2020), 29.

G.A. Anastassiou, On right fractional calculus, Chaos Solitons Fractals, 42(1) (2009), 365--376.

S. Apassara and S.N. Parinya, Existence, uniqueness, and stability of mild solutions for semilinear $psi$-Caputo fractional

evolution equations, Advances in Difference Equations, (2020), 1--28.

S. Arjumand, R. Mujeeb, A. Jehad, A. Yassine, and S.A. Mohammed, Langevin equation with nonlocal boundary conditions involving a $psi$-Caputo fractional operators of different orders, American Institute of Mathematical Sciences, 6(7) (2021), 6749--6780.

A. Atangana, Convergence and stability analysis of a novel iteration method for fractional biological population equation, Neural Computing and Applications, 25(5) (2014), 1021--1030.

C. Benzarouala and C. Tunç, Hyers–Ulam–Rassias stability of fractional delay differential equations with Caputo derivative, Mathematical Methods in the Applied Sciences, (2024).

Y. Chen, Representation of solutions and finite‐time stability for fractional delay oscillation difference equations, Mathematical Methods in the Applied Sciences, 47 (6) (2024), 3997--4013.

V. Devaraj, E.M. Elsayed, and K. Kanagarajan, On the oscillation of fractional differential equations via $psi$-Hilfer fractional derivative, Engineering and Applied Science Letters, 2(3) (2019), 1--6.

V. Devaraj, E.M. Elsayed, and K. Kanagarajan, Existence and uniqueness result for $psi$-Caputo fractional integrodifferential equations with boundary conditions, Publications de l'Institut Mathematique, 107(121) (2020), 145--155.

R. Dhayal, J.F. Gómez-Aguilar, E. and Pérez-Careta, Stability and controllability of $psi$-Caputo fractional stochastic differential systems driven by Rosenblatt process with impulses, International Journal of Dynamics and Control, 12(5) (2024), 1626--1639.

S.B. Fatima, B. Maamar, and B. Mouffak, Existence and attractivity results for $psi$-Hilfer hybrid fractional differential equations, CUBO, A Mathematical Journal, 23(1) (2021), 145--159.

L. Gaul, P. Klein, and S. Kemple, Damping description involving fractional operators, Mechanical Systems and Signal Processing, 5(2) (1991), 81--88.

W.G. Glockle and T.F. Nonnenmacher, A fractional calculus approach to self-similar protein dynamics, Biophysical Journal, 68 (1) (1995), 46--53.

A.W. Hanan, K.P. Satish, and S.A. Mohammed, Existence and stability of a nonlinear fractional differential equation involving a $psi$-Caputo operator, Advances in the Theory of Nonlinear Analysis and its Applications, 4 (2020), 266--278.

S. Harikrishnan, S. Kamal, and K. Kanagarajan, Study of a boundary value problem for fractional order $psi$-Hilfer fractional derivative, Arabian Journal of Mathematics, 9 (2020), 589--596.

Z. Odibat and D. Baleanu, Numerical simulation of nonlinear fractional delay differential equations with Mittag-Leffler kernels, Applied Numerical Mathematics, 201 (2024), 550--560.

A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, (2006).

V. Lakshmikantham, Theory of fractional functional differential equations, Nonlinear Analysis, 69 (2008), 3337--3343.

F. Mainardi, Fractional calculus: some basic problems in continuum and statistical mechanics, Fractals and Fractional Calculus in Continuum Mechanics, (1997), 291--348.

R. Metzler, W. Schick, H.G. Kilian, and T.F. Nonnenmacher, Relaxation in filled polymers: a fractional calculus approach, International Journal of Chemical Physics, 103 (1995), 7180--7186.

A.A. Mohammed and K.P. Satish, Existence results of $psi$-Hilfer integrodifferential equations with fractional order in Banach space, Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica, 19 (2020), 171--192.

S.A. Mohammed and K.P. Satish, Fractional boundary value problem with $psi$-Caputo fractional derivative, Proceedings Mathematical Sciences, 129 (2019), 63--65.

S.A. Mohammed, K.P. Satish, and S.H. Hussien, Fractional integrodifferential Equations with nonlocal conditions and $psi$-Hilfer fractional derivative, Mathematical Modeling and Analysis, 24(4) (2019), 564--584.

K.B. Oldham and J. Spanier, The Fractional Calculus: Theory and applications of differentiation and integration to

arbitrary Order, Mathematics in Science and Engineering, Academic Press, New York (1974).

D. Prabu, P. Sureshkumar, and N. Annapoorani, Controllability of nonlinear fractional Langevin systems using

$Psi$-Caputo fractional derivative, International Journal of Dynamics and Control, 12 (2024), 190--199.

K. Shah, G. Ali, K.J. Ansari, T. Abdeljawad, M. Meganathan, and B. Abdalla, On qualitative analysis of boundary value problem of variable order fractional delay differential equations, Boundary Value Problems, 1 (2023), 55p.

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Published

07-11-2024

How to Cite

D, P. (2024). Existence and stability results for $\psi$-Caputo fractional integrodifferential equations with delay. Hilbert Journal of Mathematical Analysis, 2(2), 106–117. https://doi.org/10.62918/hjma.v2i2.26