On fractional backward differential formulas for fractional delay differential equations with periodic and anti-periodic conditions

A Novel Shifted Jacobi Operational Matrix Method for Linear Multi-terms Delay Differential Equations of Fractional Variable-order with Periodic and Anti-periodic Conditions

“…Currently, it has become an important tool because of its vast applications in different scientific fields for example, physics, chemistry, blood circulation phenomena, electrodynamics, biophysics, capacitor theory, Complex environment, polymer rheology, experimental data fitting, dynamic systems, etc. (see [4][5][6][7]11] and references therein). The increasing development of efficient and suitable methods with high accuracy to solve F DEs has caused the interest of many researchers to increase in this field.…”

“…Fractional DDEs differ from the ordinary type in which the derivative at any time depends on the solution (and when the equations are neutral then related to the derivative) at previous times. Many real-world happenings can be modeled as the F DDEs [11]. The F DDEs have many usages in different scientific areas by modeling different problems like electro dynamics, economy, biology, finance, control, physics, chemistry and etc.…”

A novel shifted Jacobi operational matrix method for nonlinear multi‐terms delay differential equations of fractional variable‐order with periodic and anti‐periodic conditions

“…Many real-world events can be modeled as the delay fractional differential equations. 4 The fraction order of differential equations has many application in various scientific disciplines by modeling of various problem such as economy, electro dynamics, biology, control, finance, chemistry, physics, and so on; for further reading, interested parties can refer to reader to the previous literature 14,[17][18][19][20][21][22] resources.…”

“…The applications and analysis of fractional order calculus are active and the fastest growing regions for research in the last three decades. It has currently become an important tool owing to their wide usages in diverse scientific disciplines, such as chemistry, physics, regular changes in thermodynamics, blood circulation phenomenons, biophysics, electro‐dynamics of complex medium, capacitor theory, polymer rheology, dynamical systems, fitting of experimental data, and so forth (previous studies 1–4 and references therein). The increasing development of appropriate and efficient method to solve $$$ FDE $$$s have aroused more interest of researchers in this field.…”

“…Fractional delay differential equations are different from the ordinary type in which the derivative at any time related to the solution (and when the equations are neutral then depends on the derivative) at previous times. Many real‐world events can be modeled as the delay fractional differential equations 4 . The fraction order of differential equations has many application in various scientific disciplines by modeling of various problem such as economy, electro dynamics, biology, control, finance, chemistry, physics, and so on; for further reading, interested parties can refer to reader to the previous literature 14,17–22 resources.…”