Nonlinear functional differential equations of arbitrary orders

Numerical solution for multi-term fractional (arbitrary) orders differential equations

“…The existence of at least one solution of this initial value problem has been proved (see [13]) where the function f (t, U) = f (t, u 1 (t), ..., u n (t)) satisfies Caratheodory conditions, i.e., t → f (t, U) is measurable for every U ∈ R n+1 and U → f (t, U) is continuous for every t ∈ I . f (t, U) is nondecreasing for all variables, and there exist a function a(t) ∈ L 1 and constants b k ≥ 0, such that…”

“…(β) for t > 0, φ β (t) = 0 for t ≤ 0 and φ β → δ(t) (the delta function) as β → 0 (see [16] [2], [13], [18], [24] and [27]) …”

Existence and Uniqueness for the Boundary Value Problems of Nonlinear Fractional Differential Equation

“…This paper considers the following boundary value problems of fractional order differential equations ( ) Podlubny [3], Hilfer [5] and the papers of Agarwal et al [6], El-Sayed [7] [8] [9] [10], Benchohra et al [11] [12], Yu and Gao [13] [14], Zhang [15], He [4] and the others references therein [16]- [23].…”

Dynamics of Salmonella Infection

“…Fractional-order (or free-order) differential models have been successfully applied to system biology, physics, chemistry, and biochemistry, hydrology, medicine, and finance (see, e.g., [6][7][8][9][10][11][12] and the references therein). In many cases, they are more contestant with the real phenomena than the integer-order models, because the fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes.…”