Ulam stability for nonlinear-Langevin fractional differential equations involving two fractional orders in the ψ-Caputo sense

Existence and Ulam–Hyers stability results for nonlinear fractional Langevin equation with modified argument

“…Definition 3. Equation ( 1) is Ulam-Hyers stable if there exists a real number c > 0 such that for each 𝜀 > 0 and for each solution 𝜗 ∈ C([−r, T], R) of the inequality 30 For 𝛼, 𝜃 > 0, we have…”

“…We mention here some papers. [20][21][22][23][24][25][26][27][28][29][30] This paper deals with the existence and uniqueness of solutions as well as the Ulam-Hyers stability for the following nonlinear fractional-order Langevin equation with a modified argument:…”

“…Recently, the existence‐uniqueness and stability results for nonlinear fractional Langevin equations are studied. We mention here some papers 20–30 …”

Some Qualitative Analyses of Neutral Functional Delay Differential Equation with Generalized Caputo Operator

“…Almeida [20] introduced a new fractional derivative, named the ψ-fractional order derivative (FOD), with respect to another function, which extended the classical fractional derivative. Therefore, the generalizations of existing results in fractional calculus and FBVPs have been established by several mathematicians [21][22][23][24][25].…”

Existence and U-H-R Stability of Solutions to the Implicit Nonlinear FBVP in the Variable Order Settings

“…Fractional calculus has recently been discussed in various research works in multidisciplinary sciences due to its powerful applicability in modeling various scientific phenomena due to the property of the nonlocality and memory effect that some physical systems exhibit. Therefore, some interesting research works concerning the mathematical analysis and applications of fractional calculus have been discussed in [1][2][3][4][5][6][7][8][9][10][11][12][13]. The fractional calculus of variable order extends the theory of the constant order one.…”