Existence of solutions for a class of Caputo tempered fractional derivative equations with boundary value problems
Abstract
The existence of solutions to a specific class of boundary -valued Caputo tempered fractional differential equations is the subject of this work. Furthermore, we illustrate our results, with some examples.
References
Abbas MI. On the coupled system of tempered fractional differential equations with anti-periodic
boundary conditions. In: Debnath P, et al., editors. Fixed Point Theory and Fractional Calculus.
Forum for Interdisciplinary Mathematics. Springer; 2022. p. 211–228. doi:10.1007/978-981-19-0668-
_12
Agarwal RP, Meehan M, O’Regan D. Fixed point theory and applications. Cambridge Tracts in
Mathematics 141. Cambridge: Cambridge University Press; 2001.
Benchohra M, Hamani S, Ntouyas SK. Boundary value problems for differential equations with fractional
order. Surv Math Appl. 2008;3:1–12.
Diethelm K. The analysis of fractional differential equations: an application-oriented exposition using
differential operators of Caputo type. Lecture Notes in Mathematics, vol. 2004. Berlin: Springer; 2010.
Khuddush M, Prasad KR. Existence, uniqueness and stability analysis of a tempered fractional order
thermistor boundary value problems. J Anal. 2023;31:85–107.
Kilbas AA, Srivastava HM, Trujillo JJ. Theory and applications of fractional differential equations.
North-Holland Mathematics Studies, 204. Amsterdam: Elsevier Science B.V.; 2006.
Ledesma CET, Cuti H, Rodríguez JA, Bonilla MM. Boundary value problem with tempered fractional
derivatives and oscillating term. J Pseudo-Differ Oper Appl. 2023;14:62, 25 pages.
Li C, Deng W, Zhao L. Well-posedness and numerical algorithm for the tempered fractional ordinary
differential equations. Discrete Contin Dyn Syst. 2019;24(4):1989–2015.
Morgado ML, Rebelo M. Well-posedness and numerical approximation of tempered fractional terminal
value problems. Fract Calc Appl Anal. 2017;20(5):1239–1262.
Mouhous A, Georgiev SG, Mebarki K. Existence of solutions for a class of first order boundary value
problems. Arch Math. 2022;58(3):141–158.
Samko SG, Kilbas AA, Marichev OI. Fractional integrals and derivatives. Theory and applications.
Yverdon: Gordon and Breach; 1993.
Tisdell CC. Existence of solutions to first-order periodic boundary value problems. J Math Anal Appl.
;323:1325–1332.
Tisdell CC. On the solvability of nonlinear first-order boundary value problems. Electron J Differential
Equations. 2006;2006(80):1–8.
Zaky MA. Existence, uniqueness and numerical analysis of solutions of tempered fractional boundary
value problems. Appl Numer Math. 2019;145:429–457.
